Phase-Transition Theory of Instabilities. II. Fourth-Harmonic Bifurcations and lambda -Transitions

The cosmological QCD phase transitions may have taken place between 10-5 s and 10-4 s in the early universe offers us one of the most intriguing and fascinating questions in cosmology. In bag models, the phase transition is described by the first-order phase transition and the role played by the latent heat or energy released in the transition is highly nontrivial and is being classified as the first-order phase transition. In this presentation, we assume, first of all, that the cosmological QCD phase transition, which happened at a time between 10-5 s and 10-4 s or at the temperature of about 150 MeV and accounts for confinement of quarks and gluons to within hadrons, would be of first-order. Of course, we may assume that the cosmological QCD phase transition may not be of the first-order. To get the essence out of the first-order scenario, it is sufficient to approximate the true QCD vacuum as one of possibly degenerate vacua and when necessary we try to model it effectively via a complex scalar field with spontaneous symmetry breaking. On the other hand, we may use a real scalar field in describing the non-first-order QCD phase transition. In the first-order QCD phase transition, we could examine how and when pasted or patched domain walls are formed, how long such walls evolve in the long run, and we believe that the significant portion of dark matter could be accounted for in terms of such domain-wall structure and its remnants. Of course, the cosmological QCD phase transition happened in the way such that the false vacua associated with baryons and many other color-singlet objects did not disappear (that is, using the bag-model language, there are bags of radius 1.0 fermi for the baryons) — but the amount of the energy remained in the false vacua is negligible by comparison. The latent energy released due to the conversion of the false vacua to the true vacua, in the form of pasted or patched domain walls in the short run and their numerous evolved objects, should make the concept of the radiation-dominated epoch, or of the matter-dominated epoch to be reexamined.

The first-order phase transition of ethane confined in MCM-41, i.e., capillary condensation, has been measured using an isochoric cooling procedure by differential scanning calorimetry (DSC) under conditions ranging from 206 K and 1.1 bar up to the pore critical point (PCP). The PCP has also been determined using the three-line method developed earlier based on the vanishing heat of phase transition. As in the bulk phase, no first-order phase transition can occur above the critical point, which also implies that vapor can transform into liquid gradually by following a path around the critical point through the supercritical region. For the first time, the gradual phase transition is demonstrated with ethane in MCM-41, which is achieved through a multistep process with paths proceeding around the PCP without crossing the capillary-condensation curve. The occurrence of the gradual phase transition in nanopores, thus the confined supercriticality, is confirmed while our consistent DSC measurements are also well demonstrated.

The review is devoted to an analysis of the influence of typical factors present in a real experiment (impurities, phonons, domain structure, etc.) on the behavior of thermodynamic quantities near a second-order phase transition point. Chapter II discusses equilibrium thermodynamic perturbations. Perturbations that differ in nature are considered from a unified point of view in which the idea of isomorphism is used. In the first stage, in each concrete case, thermodynamic variables called isomorphic are introduced, in which the ordinary second-order phase transition takes place. It is frequently difficult or impossible, however, to carry out an experiment in which the isomorphic variables remain constant. The second stage therefore consists of a transition from isomorphic variables to experimental variables, which can be conveniently maintained constant in the experiment. In terms of the experimental variables, the picture of the phase transition can differ strongly from the usual picture of a second-order phase transition. Thus, in the case of impurities, if the measurements are carried out at constant concentration, a third-order phase transition takes place, and if the ordering parameter interacts with longitudinal or transverse phonons (at constant pressure), the phase transition is of first order. Chapter III discusses the influence of nonequilibrium perturbations (mainly immobile impurities and inhomogeneities) on the thermodynamics of the phase transitions. In this case there may exist several (at least two) points that are nonanalytic in the temperature and have weak singularities of the thermodynamic quantities. A temperature interval of the smearing of the transition is indicated for each type of perturbation. The theory is compared with experiment.

In many particle physics models, domain walls can form during the phase transition process after the breakdown of the discrete symmetry. Utilizing the ℤ3 symmetric complex singlet scalar extension of the Standard Model, we study the gravitational waves produced by the strongly first-order electroweak phase transition and the domain wall decay. The gravitational wave spectrum is of a typical two-peak shape. The high frequency peak corresponding to the strongly first-order electroweak phase transition is able to be probed by the future space-based interferometers, and the low frequency peak coming from the domain wall decay is far beyond the capability of the current Pulsar Timing Arrays, and future Square Kilometer Array.

The occurrence of first-order dimer phase transitions (PT) in quasi-one-dimensional lattice coupled anisotropic spin systems and one- and two-band Hubbard systems is studied. It is shown that a certain degree of exchange anisotropy of the $s=\frac{1}{2}$ Heisenberg chains is needed to obtain first-order PT. The first-order spin-dimer PT of the zig-zag chains in V${\mathrm{O}}_{2}$ is explained as a consequence of geometric constraints. The first-order metal-insulator PT observed in V${\mathrm{O}}_{2}$ is explained by means of the two-band Hubbard model. For the charge-transfer salts it is argued that a polarization instability is associated with the first-order spin-dimer PT which requires the isotropic Heisenberg model to be modified. The so far unexplained magnetic-excitation gap observed in uniformly stacked tetramethyl-$p$-phenylenediamine-tetracyanoquinodimethane (TMPD-TCNQ) crystals is attributed to a spin-polarization instability.

The phase transition in the polarization switching (PS) of vertical-cavity surface-emitting lasers (VCSELs) was recently reported to be a second-order phase transition (SOPT). However, some features of this phase transition indicate that the VCSEL’s PS (VPS) is different from the traditional SOPTs. Most of the phase transition investigations of the laser employ the laser’s intensity as the order parameter. In Landau’s paradigm, that parameter evolutes from zero to non-zero values, or vice versa, during SOPTs, corresponding to a transition between a disordered phase and an ordered phase. Nevertheless, in the VPS, the laser’s intensity remains constant before and after the PS, revealing an order-to-order transition. Furthermore, the laser’s transverse modes cannot transfer to each other through continuous deformations in geometry. That feature attributes a topological characteristic to the laser’s transverse modes. The spatial coherence of the laser also implements a globally geometric characteristic to the laser’s output. Accordingly, there are two similarities between the VPS and quantum phase transitions (QPTs) with topological order. First, both of them belong to the orderto- order phase transitions. Second, in both transitions, two ground states are orthogonal, and are degenerate at the critical point. This paper investigated the analogy between the QPT with topological order and the VPS, exploring that the VPS has a potential to simulate the QPTs of other physical systems.

view Abstract Citations (99) References (21) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS On Large-Scale Instabilities during Gravitational Collapse and the Evolution of Shrinking Maclaurin Spheroids. Lynden-Bell, D. Abstract The collapse of a rotating, pressureless, sell-gravitating spheroid is computed and shown to be unstable against small second harmonic deformation throughout the period of collapse into a disk. The disk actually formed may thus be considerably elongated along a diameter. This may be significant in the formation of galaxies. The instability due to friction that occurs in the classical sequence of Maclaurin spheroids at their point of bifurcation with the Jacobi ellipsoids only develops if the spheroid is shrinking more slowly than the rate at which viscosity can dissipate the energy. Small tides raised by another body have little effect except when they resonate at a natural frequency of the spheroid. Chandrasekhar's virial tensor method can be used to discuss time-varying ellipsoids provided the velocities are linear functions of position. Publication: The Astrophysical Journal Pub Date: May 1964 DOI: 10.1086/147860 Bibcode: 1964ApJ...139.1195L full text sources ADS |

To understand the mechanism of first-order magnetic phase transition in ordered FeRh thin films, the magnetic properties and first-order antiferromagnetic (AFM)–ferromagnetic (FM) phase transition behavior of single-crystal FeRh thin film are investigated in detail. The first-order magnetic phase transition is seen at a temperature of around 120 °C during heating and 145 °C cooling processes in perpendicular direction. The M–H loops measured isothermally amidst the AFM–FM transition regime show an opening at high magnetic field, which indicate a reversible AFM–FM transition induced by magnetic field. The clusters of the FM phase nucleate in the AFM matrix heterogeneously and vice versa during the first-order phase transition and the mechanism of nucleation and growth kinetics of the first-order magnetic phase transition in ordered FeRh thin film is quite similar to that of the crystallization of solids described by the Avrami model.

The Ginzburg-Landau theory is developed to investigate coupling between a gas-liquid first-order phase transition (FOPT) and an orientational second-order phase transition (SOPT) in Langmuir monolayers. It is found that the coupled SOPT and FOPT takes place simultaneously if the uncoupled FOPT occurs prior to the SOPT with compression, and that in the opposite case, the coupling makes the FOPT take place at a lower pressure, but still behind the SOPT. Gas-liquid phase separation always leads to a decrease in the averaged order parameter of the orientational phase transition, which is qualitatively consistent with experimental data.

In this work, we discuss the deconfinement phase transition to quark matter in hot/dense matter. We examine the effect that different charge fractions, isospin fractions, net strangeness, and chemical equilibrium with respect to leptons have on the position of the coexistence line between different phases. In particular, we investigate how different sets of conditions that describe matter in neutron stars and their mergers, or matter created in heavy-ion collisions affect the position of the critical end point, namely where the first-order phase transition becomes a crossover. We also present an introduction to the topic of critical points, including a review of recent advances concerning QCD critical points.

The structure of annealed and quenched models with localU(1) gauge invariance is studied in terms of the Helmholtz free energy. The first non-trivial, or one-loop, account of fluctuations in the annealed model suggests that spontaneous symmetry breaking occurs in two and three dimensions, through a first-order phase transition. Within the same approximation scheme, the quenched model displays a continuous phase transition. A more complete account of the fluctuations in the annealed model changes the nature of the transition to a continuous one, whereas spontaneous symmetry breaking is then absent with quenched disorder.

We propose a theoretical model to study the quantum phase transition in a double-cavity magnonic system. We find that the system exhibits a second-order phase transition from a parity-symmetric phase to a parity-symmetry-broken phase or a first-order phase transition from a parity-symmetric phase to a bistable phase when the driving strength of one cavity is above a critical value. We obtain the phase diagram, the critical point, and the corresponding critical exponent to characterize the phase transition. We can identify different phase transitions by the different behaviors of the mean magnon number and correlation fluctuation in the vicinity of the critical point. In particular, we show that the phase transition in one cavity can be precisely and efficiently controlled by adjusting the parameters of the other cavity, which suggests that we can easily observe the phase transition at low driving strength in experiment. The effects of additional microwave pulses on the dynamical behavior of the phase-transition observable and the experimental feasibility of our theoretical scheme are discussed as well.

The generalized Replica Exchange Method (gREM) is extended into the isobaric-isothermal ensemble, and applied to simulate a vapor-liquid phase transition in Lennard-Jones fluids. Merging an optimally designed generalized ensemble sampling with replica exchange, gREM is particularly well suited for the effective simulation of first-order phase transitions characterized by "backbending" in the statistical temperature. While the metastable and unstable states in the vicinity of the first-order phase transition are masked by the enthalpy gap in temperature replica exchange method simulations, they are transformed into stable states through the parameterized effective sampling weights in gREM simulations, and join vapor and liquid phases with a succession of unimodal enthalpy distributions. The enhanced sampling across metastable and unstable states is achieved without the need to identify a "good" order parameter for biased sampling. We performed gREM simulations at various pressures below and near the critical pressure to examine the change in behavior of the vapor-liquid phase transition at different pressures. We observed a crossover from the first-order phase transition at low pressure, characterized by the backbending in the statistical temperature and the "kink" in the Gibbs free energy, to a continuous second-order phase transition near the critical pressure. The controlling mechanisms of nucleation and continuous phase transition are evident and the coexistence properties and phase diagram are found in agreement with literature results.

In this paper, we investigate the mixed-state entanglement in a model of p-wave superconductivity phase transition using holographic methods. We calculate several entanglement measures, including holographic entanglement entropy (HEE), mutual information (MI), and entanglement wedge cross-section (EWCS). Our results show that these measures display critical behavior at the phase transition points, with the EWCS exhibiting opposite temperature behavior compared to the HEE. Furthermore, we explore the behavior of thermodynamics and holographic quantum information at the zeroth-order phase transition point and find that it is opposite to that observed in the first-order phase transition. Additionally, we find that the critical exponents of all entanglement measures are twice those of the condensate. Our findings also suggest that the EWCS is a more sensitive indicator of the critical behavior of phase transitions than the HEE. Lastly, we uncover a universal inequality in the growth rates of EWCS and MI near critical points in thermal phase transitions, such as p-wave and s-wave superconductivity, suggesting that MI captures more information than EWCS when a phase transition first occurs.

In recent years, the interest of both experimentalists and theoreticians in phase transitions has been centered on the non-analytic behavior of thermodynamic and other properties in the neighborhood of a critical point or continuous phase transition [1]. In pursuing this interest it has been easy to lose sight of the fact that global features of many phase transitions are satisfactorily described by a physical picture which in the context of liquid-vapor phase transitions is called the Van der Waals theory, and in the context of magnetism, the mean-field theory. This physical picture is exact for the weak long range force model in which the forces are infinite ranged but weak in such a way that the product of the potential and the volume in which the force operates is finite [2]. Recently, in the course of an attempt to apply the scaling theory of critical phenomena and its extensions to the liquid-vapor transition in SF6 by M. Ley-Koo and the author [3], it became apparent that the Van der Waals theory may be more than a qualitative guide but may rather form the basis for a quantitative representation of the data to within a few percent of the critical density. It would appear that an adequate theory of the liquid-vapor phase transition requires a model with short range forces near the critical point and the weak long range force model far from the critical point.