**discontinuous at the transition**- Under this scheme, phase transitions were labeled by the lowest derivative of the free energy that is discontinuous at the transition. (wikipedia.org)
- See phase transition for Ehrenfest's classification of phase transitions by the derivative of free energy which is discontinuous at the transition). (wikipedia.org)

**vapor phase**- When water vapor condenses (an equilibrium fractionation), the heavier water isotopes (18O and 2H) become enriched in the liquid phase while the lighter isotopes (16O and 1H) tend toward the vapor phase. (wikipedia.org)
- Sublimation is caused by the absorption of heat which provides enough energy for some molecules to overcome the attractive forces of their neighbors and escape into the vapor phase. (wikipedia.org)

**diagrams**- Starting from a given interparticle pair potential we predict the corresponding phase diagrams using computer simulations, cell theory, and density functional theory. (ebscohost.com)
- We investigate the phase diagrams for cases of different atom numbers on resonance by making use of the mean-field approximation and find that both the fidelity and entanglement entropy for the ground state have dramatic changes near the critical points. (osapublishing.org)
- Low-Temperature Properties of Classical Lattice Systems: Phase Transitions and Phase Diagrams', by J. Slawny. (wikipedia.org)
- Many of these contributions have been linked to experiments, especially to the rich phase diagrams of the high temperature superconductors. (wikipedia.org)

**ferromagnetic**- The transition between the ferromagnetic and paramagnetic phases of magnetic materials at the Curie point. (wikipedia.org)
- For the aforementioned ferromagnetic transition, the order parameter would represent the total magnetization of the system. (wikipedia.org)
- In analogy to ferromagnetic and paramagnetic materials, the Curie temperature can also be used to describe the phase transition between ferroelectricity and paraelectricity. (wikipedia.org)
- Below the Curie temperature the intrinsic structure has undergone a phase transition, the atoms are ordered and the material is ferromagnetic. (wikipedia.org)

**crystalline**- A Finnish-Japanese joint research project has produced first-rate results by discovering a phase transition in the structure of crystalline materials in atomistic simulations. (innovations-report.com)
- The results achieved in the project, however, suggest that it may in semiconductors be a question of a crystalline-to-crystalline phase transition. (innovations-report.com)
- Phase transitions between the cholesteric and high density liquid crystalline DNA phases occur with the formation of batonnets during unwinding of the cholesteric mesophase. (fsu.edu)
- The electronic and optical properties of the low and high-pressure phases of crystalline MgH 2 were calculated. (diva-portal.org)

**Curie**- Talking about quantum phase transitions means talking about transitions at T = 0: by tuning a non-temperature parameter like pressure, chemical composition or magnetic field, one could suppress e.g. some transition temperature like the Curie or Néel temperature to 0 K. As a system in equilibrium at zero temperature is always in its lowest-energy state, a QPT cannot be explained by thermal fluctuations. (wikipedia.org)
- The transition from antiferromagnetic to paramagnetic (or vice versa) occurs at the Néel temperature which is analogous to Curie temperature. (wikipedia.org)
- α phase being most phase for pure GeTe below the ferroelectric Curie temperature of approximately 670 K. Doped germanium telluride is a low temperature superconductor. (wikipedia.org)

**topological**- Examples include: quantum phase transitions, dynamic phase transitions, and topological (structural) phase transitions. (wikipedia.org)
- According to the authors this indicates a topological phase transition and they then proceed to show that a Majorana edge state forms centered around the point, where the closes. (physicsforums.com)
- What does a topological phase transition mean and what indicates that we are dealing with a topological phase transition? (physicsforums.com)
- However for a topological phase transition you don't have this. (physicsforums.com)
- When you go through a topological phase transition, this winding number changes. (physicsforums.com)

**Subir**- Quantum phase transition Classical phase transitions Quantum critical point Sachdev, Subir (2000). (wikipedia.org)

**thermodynamic**- A phase of a thermodynamic system and the states of matter have uniform physical properties. (wikipedia.org)
- Phase transitions occur when the thermodynamic free energy of a system is non-analytic for some choice of thermodynamic variables (cf. phases). (wikipedia.org)
- It is important to note that phase transitions can occur and are defined for non-thermodynamic systems, where temperature is not a parameter. (wikipedia.org)
- Paul Ehrenfest classified phase transitions based on the behavior of the thermodynamic free energy as a function of other thermodynamic variables. (wikipedia.org)
- First-order phase transitions exhibit a discontinuity in the first derivative of the free energy with respect to some thermodynamic variable. (wikipedia.org)
- Deposition is a thermodynamic process, a phase transition in which gas transforms into solid without passing through the liquid phase. (wikipedia.org)

**Sachdev**- Sachdev argued instead that it is better to examine how rapidly the system loses quantum phase coherence, or reaches local thermal equilibrium in response to general external perturbations. (wikipedia.org)

**colloid**- Structure and phase transitions in confined binary colloid mixtures. (ebscohost.com)

**order parameter**- You think about phase transitions in terms of an order parameter. (physicsforums.com)
- These continuous transitions from an ordered to a disordered phase are described by an order parameter, which is zero in the disordered and nonzero in the ordered phase. (wikipedia.org)
- The order parameter plays a role in quantum phases analogous to its role in classical phases. (wikipedia.org)

**equilibrium**- Photoinduced phase transition is a process to the nonequilibrium phases generated from an equilibrium by shining on high energy photons, and the nonequilibrium phase is a macroscopic excited domain that has new structural and electronic orders quite different from the starting ground state (equilibrium phase). (wikipedia.org)
- The behavior of incubation time deviated from that in equilibrium, indicating a different physical origin of the transition barrier in this system. (nyu.edu)
- Phase equilibrium has been considered within the context of their physical similarities, with appropriate scaling, to elastic solids. (wikipedia.org)

**describe**- The term phase transition (or phase change) is most commonly used to describe transitions between solid, liquid and gaseous states of matter, and, in rare cases, plasma (physics). (wikipedia.org)
- Sublimation has also been used as a generic term to describe a solid-to-gas transition (sublimation) followed by a gas-to-solid transition (deposition). (wikipedia.org)
- I will describe a new spectral algorithm based on the non-backtracking matrix, which avoids these localized eigenvectors: it appears to be optimal in the sense that it succeeds all the way down to the transition. (princeton.edu)

**gaseous**- Examples of phase transitions include: The transitions between the solid, liquid, and gaseous phases of a single component, due to the effects of temperature and/or pressure: v t e (see also vapor pressure and phase diagram) A eutectic transformation, in which a two component single phase liquid is cooled and transforms into two solid phases. (wikipedia.org)
- In these cases, the transition from the solid to the gaseous state requires an intermediate liquid state. (wikipedia.org)

**particles**- The results are explained with allowance for the magnetic moment relaxation in single-domain particles and phase transitions in a system of. (ebscohost.com)

**abrupt change**- The transition describes an abrupt change in the ground state of a many-body system due to its quantum fluctuations. (wikipedia.org)
- A phase transition is an abrupt change between different structures of passive or active constitutes, with snow formation, graphite-diamond transition and emergence of bird flocking as common examples. (nyu.edu)

**atoms**- In quantum optics, a superradiant phase transition is a phase transition that occurs in a collection of fluorescent emitters (such as atoms), between a state containing few electromagnetic excitations (as in the electromagnetic vacuum) and a superradiant state with many electromagnetic excitations trapped inside the emitters. (wikipedia.org)
- The superradiant phase transition was originally predicted by the Dicke model of superradiance, which assumes that atoms have only two energetic levels and that these interact with only one mode of the electromagnetic field. (wikipedia.org)
- The phase transition occurs when the strength of the interaction between the atoms and the field is greater than the energy of the non-interacting part of the system. (wikipedia.org)
- However, both the original derivation and the later corrections leading to nonexistence of the transition - due to Thomas-Reiche-Kuhn sum rule canceling for the harmonic oscillator the needed inequality to impossible negativity of the interaction - were based on the assumption that the quantum field operators are commuting numbers, and the atoms do not interact with the static Coulomb forces. (wikipedia.org)

**ISBN**- Volume 1: Exact Results (1972) ISBN 0122203011 'Introductory Note on Phase Transitions and Critical Phenomena', by C.N. Yang. (wikipedia.org)
- Volume 5b (1976) ISBN 0122203054 'Monte Carlo Investigations of Phase Transitions and Critical Phenomena', by K. Binder. (wikipedia.org)
- Volume 7: (1983) ISBN 0122203070 'Defect-Mediated Phase Transitions', by D.R. Nelson. (wikipedia.org)
- Critical Point Statistical Mechanics and Quantum Field Theory', by G.A. Baker, Jr. Volume 10: (1986) ISBN 0122203100 'Surface Structures and Phase Transitions - Exact Results', by D.B. Abraham. (wikipedia.org)
- Volume 11: (1987) ISBN 0122203119 'Coulomb Gas Formulation of Two-Dimensional Phase Transitions', by B. Nienhus. (wikipedia.org)

**occur**- A classical system does not have entropy at zero temperature and therefore no phase transition can occur. (wikipedia.org)

**Experimentally**- Experimentally, the 'quantum critical' phase, which is still governed by quantum fluctuations, is the most interesting one. (wikipedia.org)
- Both of these phases have been experimentally observed in ultracold atomic gases. (wikipedia.org)

**mesophase**- Transition to a mesophase between solid and liquid, such as one of the "liquid crystal" phases. (wikipedia.org)

**separates**- A spinodal decomposition, in which a single phase is cooled and separates into two different compositions of that same phase. (wikipedia.org)
- From a theoretical point of view, a phase diagram like the one shown on the right is expected: the QPT separates an ordered from a disordered phase (often, the low temperature disordered phase is referred to as 'quantum' disordered). (wikipedia.org)
- An example of a canonical quantum phase transition is the well-studied Superconductor Insulator Transition in disordered thin films which separates two quantum phases having different symmetries. (wikipedia.org)

**structures**- The transition between differently ordered, commensurate or incommensurate, magnetic structures, such as in cerium antimonide. (wikipedia.org)
- The transition between different molecular structures (polymorphs, allotropes or polyamorphs), especially of solids, such as between an amorphous structure and a crystal structure, between two different crystal structures, or between two amorphous structures. (wikipedia.org)
- Colloidal crystals are receiving increased attention, largely due to their mechanisms of ordering and self-assembly, cooperative motion, structures similar to those observed in condensed matter by both liquids and solids, and structural phase transitions. (wikipedia.org)

**structural phase**- Here, the pressure-induced structural phase transformations of NaBH 4 and ErH 3 were investigated. (diva-portal.org)

**transformations**- Transformations connecting one Kuryshkin's algebras class to another are degenerated so that the transition from one class of equivalency to another is similar to a phase transition. (springer.com)
- The martensitic transformation which occurs as one of the many phase transformations in carbon steel and stands as a model for displacive phase transformations. (wikipedia.org)
- He is also credited with wider studies in synthesis of nanocomposites, phase transformations, large superheating phenomenon during melting, dissimilar joining processes, surface modifications and nanostructured magnetic alloys. (wikipedia.org)

**symmetry**- Usually we think of phase transitions in terms of symmetry breaking (Landau Ginzburg). (physicsforums.com)
- You can go from one phase to another without breaking symmetry. (physicsforums.com)
- In a superfluid phase, this symmetry is spontaneously broken. (wikipedia.org)
- The superfluid is characterized by long-range phase coherence, a spontaneous breaking of the Hamiltonian's continuous U ( 1 ) {\displaystyle U(1)} symmetry, a non-zero compressibility and superfluid susceptibility. (wikipedia.org)
- At non-zero temperature, in certain parameter regimes there will also be a regular fluid phase which does not break the U ( 1 ) {\displaystyle U(1)} symmetry and does not display phase coherence. (wikipedia.org)

**quantum fluctuations**- The QPT occurs at the quantum critical point (QCP), where quantum fluctuations driving the transition diverge and become scale invariant in space and time. (wikipedia.org)
- Even at zero temperature a quantum-mechanical system has quantum fluctuations and therefore can still support phase transitions. (wikipedia.org)
- As a physical parameter is varied, quantum fluctuations can drive a phase transition into a different phase of matter. (wikipedia.org)

**exhibit**- These phases of matter exhibit properties and symmetries which can potentially be exploited for technological purposes and the benefit of mankind. (wikipedia.org)

**displaystyle**- A phase transition from water to ice, for example, involves latent heat (a discontinuity of the internal energy U {\displaystyle U} ) and is of first order. (wikipedia.org)
- At zero temperature, the Bose-Hubbard model (in the absence of disorder) is in either a Mott insulating state at small t / U {\displaystyle t/U} , or in a superfluid state at large t / U {\displaystyle t/U} . The Mott insulating phases are characterized by integer boson densities, by the existence of an energy gap for particle-hole excitations, and by zero compressibility. (wikipedia.org)

**systems**- We review recent work on fluid-solid and solid-solid phase transitions in soft matter systems such as colloidal suspensions and star polymer solutions. (ebscohost.com)
- The metal-hydrogen systems undergo many structural and electronic phase transitions induced by changes in pressure and/or temperature and/or H-concentration. (diva-portal.org)
- The results shed new light on microscopic mechanisms of phase transitions in active systems. (nyu.edu)

**spheres**- Phase transitions and crystal buckling of long-ranged repulsive charged spheres in an electric bottle. (ebscohost.com)
- In the colloidal crystal-crystal transitions, we employed diameter-tunable microgel spheres to trigger a transition from square lattice to triangular lattice. (nyu.edu)

**fluctuations**- The classical phase transitions are driven by a competition between the energy of a system and the entropy of its thermal fluctuations. (wikipedia.org)
- Around the classical phase transition, the system is governed by classical thermal fluctuations (light blue area). (wikipedia.org)

**processes**- Processes of heat and mass transfer with phase transitions assume an important place in such modern technologies as thermal treatment and drying of materials, welding, metallurgy, heat protection, vacuum techniques, laser and electron-beam treatment of materials, and many other areas. (begellhouse.com)

**liquids**- The citation reads: for his seminal contributions to the theory of quantum phase transitions, quantum magnetism, and fractionalized spin liquids, and for his leadership in the physics community. (wikipedia.org)

**superfluid**- The superfluid transition in liquid helium is an example of this. (wikipedia.org)
- The model rose to prominence in the 1980s after it was found to capture the essence of the superfluid-insulator transition in a way that was much more mathematically tractable than fermionic metal-insulator models. (wikipedia.org)
- The Bose glass is a Griffiths phase, and can be thought of as a Mott insulator containing rare 'puddles' of superfluid. (wikipedia.org)
- The Bose glass phase is characterized by a finite compressibility, the absence of a gap, and by an infinite superfluid susceptibility. (wikipedia.org)

**sublimation**- Sublimation is the phase transition of a substance directly from the solid to the gas phase without passing through the intermediate liquid phase. (wikipedia.org)
- Sublimation is an endothermic process that occurs at temperatures and pressures below a substance's triple point in its phase diagram, which corresponds to the lowest pressure at which the substance can exist as a liquid. (wikipedia.org)
- The reverse process of sublimation is deposition or desublimation, in which a substance passes directly from a gas to a solid phase. (wikipedia.org)

**Kinetics**- The kinetics of a phase transition is essential to understand its microscopic mechanism and to control the transition rate, intermediate state and the final structure morphology. (nyu.edu)
- Here I study the kinetics of phase transitions in a passive system, crystal-crystal transitions in colloids, and in an active system, swarming transition in E. coli suspensions. (nyu.edu)

**behavior**- Although absolute zero is not physically realizable, characteristics of the transition can be detected in the system's low-temperature behavior near the critical point. (wikipedia.org)
- This quantum critical behavior manifests itself in unconventional and unexpected physical behavior like novel non Fermi liquid phases. (wikipedia.org)
- A superradiant phase transition is formally predicted by the critical behavior of the resonant Jaynes-Cummings model, describing the interaction of only one atom with one mode of the electromagnetic field. (wikipedia.org)

**undergo**- If the interaction with the field is so strong that the system collapses in the harmonic approximation and complex polariton frequencies (soft modes) appear, then the physical system with nonlinear terms of the higher order becomes the system with the Mexican hat-like potential, and will undergo ferroelectric-like phase transition. (wikipedia.org)
- While there are physically higher terms in the true system, the system in this regime will therefore undergo the phase transition. (wikipedia.org)

**suspensions**- In particular, we discuss the following aspects: a cascade of freezing transitions for confined colloids, stable one-component quasicrystals for charged colloids, reentrant melting and anisotropic solid phases for star polymer solutions and reentrant nematic ordering for suspensions of the tobacco-mosaic virus. (ebscohost.com)
- Where the linearized Poissonâ€"Boltzmann cell model fails: Spurious phase separation in charged colloidal suspensions. (ebscohost.com)

**driven**- The resulting effect may be viewed as a unique type of quantum phase transition that is driven by the size of the system rather than by an external field or coupling strength. (pnas.org)

**occurs**- The measurement of the external conditions at which the transformation occurs is termed the phase transition. (wikipedia.org)
- Isotope fractionation occurs during a phase transition, the ratio of light to heavy isotopes in the involved molecules changes. (wikipedia.org)

**critical**- Phase Transitions and Critical Phenomena is a 20-volume series of books, comprising review articles on phase transitions and critical phenomena, published during 1972-2001. (wikipedia.org)

**Deposition**- Deposition releases energy and is an exothermic phase change. (wikipedia.org)

**matter**- In physics, a quantum phase transition (QPT) is a phase transition between different quantum phases (phases of matter at zero temperature). (wikipedia.org)
- Quantum phases are quantum states of matter at zero temperature. (wikipedia.org)

**phenomena**- In this paper we first survey recent advances on phase transition phenomena which are related to natural subclasses of the recursive functions. (springer.com)

**transforms**- A peritectic transformation, in which a two component single phase solid is heated and transforms into a solid phase and a liquid phase. (wikipedia.org)

**system**- It is sometimes possible to change the state of a system diabatically (as opposed to adiabatically) in such a way that it can be brought past a phase transition point without undergoing a phase transition. (wikipedia.org)

**change**- During a phase transition of a given medium, certain properties of the medium change, often discontinuously, as a result of the change of some external condition, such as temperature, pressure, or others. (wikipedia.org)

**stable**- The resulting state is metastable, i.e., less stable than the phase to which the transition would have occurred, but not unstable either. (wikipedia.org)

**ratio**- Softening of bulk modulus and negative Poissonâ€™s ratio near the volume phase transition of polymer gels. (ebscohost.com)

**readily**- The transition can be readily understood by the use of the Holstein-Primakoff transformation applied to a two-level atom. (wikipedia.org)
- Since PE has a small headgroup and readily forms inverted micelle phases it should, according to the stalk model, promote the formation of these stalks. (wikipedia.org)

**substance**- At the phase transition point (for instance, boiling point) the two phases of a substance, liquid and vapor, have identical free energies and therefore are equally likely to exist. (wikipedia.org)

**model**- We give a complete characterisation of the phase diagram of the model, and derive several criteria of the transient and recurrent regimes for the underlying stochastic process. (dur.ac.uk)
- Specifically, there is a detectability transition in the stochastic block model, below which no algorithm can label nodes better than chance. (princeton.edu)
- It can also be shown that the phase transition for the two dimensional rotor model has the same universality class as that of antiferromagnetic Heisenberg spin models. (wikipedia.org)

**solid**- A typical example is the freezing transition of water describing the transition between liquid and solid. (wikipedia.org)
- The phase of water (i.e., whether it assumes the form of a solid, liquid, or gas) is determined by its temperature and pressure. (wikipedia.org)

**physics**- This transition was subsequently established rigorously by Mossel, Neeman, and Sly, and Massoulie.I'll explain this transition, and give an accessible introduction to Belief Propagation and the analogy with free energy and the cavity method of statistical physics. (princeton.edu)

**strongly**- Phase transition in strongly stretched polymer gels. (ebscohost.com)

**phenomenon**- Rapid phase transition or RPT is a phenomenon realized in liquefied natural gas (LNG) incidents in which LNG vaporizes violently upon coming in contact with water causing what is known as a physical explosion or cold explosion. (wikipedia.org)
- This is the phenomenon of rapid phase transition. (wikipedia.org)

**cubic**- This topic also remains controversial, and even if there is a curved structure present in the fusion process, there is debate in the literature over whether it is a cubic, hexagonal or more exotic extended phase. (wikipedia.org)

**physical**- Contrary to classical phase transitions, quantum phase transitions can only be accessed by varying a physical parameter-such as magnetic field or pressure-at absolute zero temperature. (wikipedia.org)

**Fusion**- Further evidence cited in favor of this theory is the fact that certain lipid mixtures have been shown to only support fusion when raised above the transition temperature of these inverted phases. (wikipedia.org)

**results**- In the last section we prove in addition some results which show how the asymptotic of the standard Ramsey function is affected by phase transitions for associated parameterized Ramsey functions. (springer.com)

**high**- This transition region is illustrated in the photomicrograph presented above, which demonstrates the high degree of order induced by the magnetic field. (fsu.edu)

**light**- For the active phase transition, we used gene-mutated light-control E. coli, whose locomotion can be controlled by blue light, to switch on/off their collective motions. (nyu.edu)