First-order Phase Transition Point Research Articles

Simple and accurate expressions for radial distribution functions of hard disk and hard sphere fluids

Analytical expressions for radial distribution function (RDF) are of critical importance for various applications, such as development of the perturbation theories. Theoretically, RDF expressions for odd-dimensional fluids can be obtained by solving the Percus-Yevick integral equations. But for even-dimensional cases, such as the hard disk (2D) fluid, analytical expressions are infeasible. The only 2D RDF is a heuristic expression which provides acceptable estimations for an intermediate and low density range. In this work, we employ a simple and empirical expression for the 2D RDF and the 3D RDF based on an approach proposed for the 3D RDF. The parameters are determined in such a way that the final RDF expressions are thermodynamically consistent, namely the pressure and the isothermal compressibility constraints are both satisfied. The new RDFs for the 2D and 3D hard spheres are highly accurate for the entire density range up to the first-order phase transition points. The predictions of the first coordination numbers are consistent with simulation results for the 3D fluid. Finally, by using the 2D RDF with a primitive second-order perturbation theory, the pressure-volume-temperature relation and vapor-liquid equilibrium are calculated for the 2D Lennard-Jones fluid. Comparisons with the simulation data show promising results.

Stationarity of quantum statistical ensembles at first-order phase transition points

We study the dynamics of quantum statistical ensembles at first-order phase transition points of finite macroscopic systems. First, we show that at the first-order phase transition point of the system, with an order parameter that does not commute with the Hamiltonian, any quantum state with an order parameter that has a nonzero value always evolves towards a macroscopically distinct state after a sufficiently long time. From this result, we argue that the stationarity required for statistical ensembles should be interpreted as stationarity on a sufficiently long but finite timescale. Finally, we prove that the density matrix of the squeezed ensemble, a class of generalized statistical ensembles proposed as the only concrete method of constructing phase coexistence states applicable to general quantum systems, is locally stationary on timescales diverging in the thermodynamic limit. Our results support the validity of the squeezed ensemble from a dynamical point of view and open the door to nonequilibrium statistical physics at the first-order phase transition point.

Probing the QCD phase transition with hadron multiplicity ratios

We investigate the impact of a first-order chiral phase transition and critical point on hadron multiplicity ratios. We model the dynamical expansion of the hot and dense matter created in a heavy ion collision with a Bjorken hydrodynamics expansion coupled to the explicit evolution of the chiral order parameter at center-of-mass energies from 2 to 7 GeV. Hereby, the chiral dynamics is implemented using a Langevin equation including dissipation and noise. We find a strong enhancement of the entropy-per-baryon S/A at lowest energies which is created at the non-equilibrium first-order phase transition. By mapping the initial and final S/A to a hadron resonance gas, we can quantify the shift of hadron multiplicity ratios.

Universal anomaly of dynamics at phase transition points induced by Pancharatnam-Berry phase

Dynamical anomalies are often observed near both the continuous and first-order phase transition points. We propose that the universal anomalies could originate from the geometric phase effects. A Pancharatnam-Berry phase is accumulated continuously in quantum states with the variation of tuning parameters. Phase transitions are supposed to induce an abrupt shift of the geometric phase. In our multi-level quantum model, the quantum interference induced by the geometric phase could prolong or shorten the relaxation times of excited states at phase transition points, which agrees with the experiments, models under sudden quenches and our semi-classical model. Furthermore, we find that by setting a phase shift of π, the excited state could be decoupled from the ground state by quantum cancellation so that the relaxation time even could diverge to infinity. Our work introduces the geometric phase to the study of conventional phase transitions as well as quantum phase transition, and could substantially extend the dephasing time of qubits for quantum computing.

Reconstructing particle number distributions with convoluting volume fluctuations

We propose methods to reconstruct particle distributions with and without considering initial volume fluctuations. This approach enables us to correct for detector efficiencies and initial volume fluctuations simultaneously. Our study suggests such a tool could investigate the possible bimodal structure of net-proton distribution in Au+Au collisions at sNN= 7.7 GeV as a signature of first-order phase transition and critical point of hadronic matter (Bzdak et al., 2018; Bzdak and Koch, 2019).

Analysis of liquids, gases, and supercritical fluids by a two-dimensional replica-exchange Monte Carlo method in temperature and chemical potential space.

We investigate the liquid, gas, and supercritical fluid phases of a Lennard-Jones 12-6 potential system by a two-dimensional replica-exchange method in which not only temperature but also chemical potential is exchanged. The method is referred to as the grand canonical replica-exchange method (GCREM). While one-dimensional replica exchange, which exchanges only temperature, cannot cross first-order phase transition points, GCREM can avoid this problem by making a detour in the two-dimensional parameter space. From only one simulation run, we can obtain probability distributions in the grand canonical ensemble for wide temperature and chemical potential values using the multiple-histogram reweighting techniques. We define a phase diagram near the critical point using thermodynamic quantities. Moreover, we discuss structures in each defined phase and at phase transition points.

Social contagions on interdependent lattice networks

Although an increasing amount of research is being done on the dynamical processes on interdependent spatial networks, knowledge of how interdependent spatial networks influence the dynamics of social contagion in them is sparse. Here we present a novel non-Markovian social contagion model on interdependent spatial networks composed of two identical two-dimensional lattices. We compare the dynamics of social contagion on networks with different fractions of dependency links and find that the density of final recovered nodes increases as the number of dependency links is increased. We use a finite-size analysis method to identify the type of phase transition in the giant connected components (GCC) of the final adopted nodes and find that as we increase the fraction of dependency links, the phase transition switches from second-order to first-order. In strong interdependent spatial networks with abundant dependency links, increasing the fraction of initial adopted nodes can induce the switch from a first-order to second-order phase transition associated with social contagion dynamics. In networks with a small number of dependency links, the phase transition remains second-order. In addition, both the second-order and first-order phase transition points can be decreased by increasing the fraction of dependency links or the number of initially-adopted nodes.

Inflation of the early cold Universe filled with a nonlinear scalar field and a nonideal relativistic Fermi gas

We consider a possible scenario for the evolution of the early cold Universe born from a fairly large quantum fluctuation in a vacuum with a size a 0 ≫ l P (where l P is the Planck length) and filled with both a nonlinear scalar field φ, whose potential energy density U(φ) determines the vacuum energy density λ, and a nonideal Fermi gas with short-range repulsion between particles, whose equation of state is characterized by the ratio of pressure P(n F ) to energy density e(n F ) dependent on the number density of fermions n F . As the early Universe expands, the dimensionless quantity ν(n F ) = P(n F )/e(n F ) decreases with decreasing n F from its maximum value νmax = 1 for n F → ∞ to zero for n F → 0. The interaction of the scalar and gravitational fields, which is characterized by a dimensionless constant ξ, is proportional to the scalar curvature of four-dimensional space R = κ[3P(n F )–e(n F )–4λ] (where κ is Einstein’s gravitational constant), and contains terms both quadratic and linear in φ. As a result, the expanding early Universe reaches the point of first-order phase transition in a finite time interval at critical values of the scalar curvature R = R c =–μ2/ξ and radius a c ≫ a 0. Thereafter, the early closed Universe “rolls down” from the flat inflection point of the potential U(φ) to the zero potential minimum in a finite time. The release of the total potential energy of the scalar field in the entire volume of the expanding Universe as it “rolls down” must be accompanied by the production of a large number of massive particles and antiparticles of various kinds, whose annihilation plays the role of the Big Bang. We also discuss the fundamental nature of Newton’ gravitational constant G N .

Entanglement entropy of the Q≥4 quantum Potts chain.

The entanglement entropy S is an indicator of quantum correlations in the ground state of a many-body quantum system. At a second-order quantum phase-transition point in one dimension S generally has a logarithmic singularity. Here we consider quantum spin chains with a first-order quantum phase transition, the prototype being the Q-state quantum Potts chain for Q>4 and calculate S across the transition point. According to numerical, density matrix renormalization group results at the first-order quantum phase transition point S shows a jump, which is expected to vanish for Q→4^{+}. This jump is calculated in leading order as ΔS=lnQ[1-4/Q-2/(QlnQ)+O(1/Q^{2})].

Fluctuation effects in metastable states near first-order phase transitions

Fluctuation effects at first-order phase transitions driven by changes of other-than-temperature factors like pressure, concentration or external fields are investigated by perturbation theory. The results for the fluctuation contributions to the order parameter, the internal energy and the free energy at pre-transitional states near spinodal points of first-order phase transitions are presented to the first-nonvanishing order of the expansion parameters of the theory.

Numerical study of the minimum of the thermodynamic potential of a ferroelectric barium titanate

The macroscopic polarization is the most essential concept in any phenomenological description of dielectric media. The presence of a spontaneous macroscopic polarization is the defining property of a ferroelectric material that is central to whole physics of ferroelectrics. Based solely on symmetry considerations, Landau theory can provide a reliable description of a system equilibrium behavior near a phase transition. This phenomenological approach allows giving relations between measurable quantities using a minimal set of input parameters that can be determined by comparison with physical experiment or numerical first-principles calculation. Now, the problem of true presentation of Landau-Devonshire potential for different materials is outstanding. The properties of Landau-Devonshire thermodynamic potential (TP) for ferroelectric materials in this article is investigated on the example of barium titanate. The previously approved topological method of research of nonlinear properties of ferroelectrics is applied. The cellular complexes approach use for interpretation of TP extremes. The new representation of the 8-order polynomial TP compared with previously used 6-order representation. For the 8 order potential the structure of metastable states for barium titanate is presented in the vicinity of first-order phase transition point at T = 5°C. New method proposed for the qualitative description of the metastable states structure that TP generates. Based on the method the temperature regions are pointed where the 6 and 8 order potentials predicting for the metastable states are qualitatively different.

Finite-size effects in a mean-field kinetically constrained model: dynamical glassiness and quantum criticality

On the example of a mean-field Fredrickson–Andersen kinetically constrained model, we focus on the known property that equilibrium dynamics take place at a first-order dynamical phase transition point in the space of time realizations. We investigate the finite-size properties of this first-order transition. By discussing and exploiting a mapping of the classical dynamical transition—an argued glassiness signature—to a first-order quantum transition, we show that the quantum analogy can be exploited to extract finite-size properties, which in many respects are similar to those in genuine mean-field quantum systems with a first-order transition. We fully characterize the finite-size properties of the order parameter across the first-order transition.

Effect of an external magnetic field on the dynamics of the nucleus of a new phase near the first-order phase transition in magnetics with defects

The evolution of the nucleus of a new phase near the point of a spin-reorientation first-order phase transition in its magnetics in an external magnetic field is investigated. The effect of the external field and one-dimensional magnetic anisotropy defects on the dynamics of such a nucleus is investigated. Critical fields that promote remagnetization of the sample are noted and evaluated.

Geometric Curvatures of Plane Symmetry Black Hole

We study the properties and thermodynamic stability of the plane symmetry black hole from the viewpoint of geometry. We find that the Weinhold curvature gives the first-order phase transition atN=1, whereNis a parameter of the plane symmetry black hole while the Ruppeiner one shows first-order phase transition points for arbitraryN≠1. Considering the Legendre invariant proposed by Quevedo et al., we obtain a unified geometry metric, which contains the information of the second-order phase transition. So, the first-order and second-order phase transitions can be both reproduced from the geometry curvatures. The geometry is also found to be curved, and the scalar curvature goes to negative infinity at the Davie phase transition points beyond semiclassical approximation.

Nonequilibrium dynamics of a spin-3/2 Blume-Capel model with quenched random crystal field

The relaxation and complex magnetic susceptibility treatments of a spin-3/2 Blume-Capel model with quenched random crystal field on a two-dimensional square lattice are investigated by a method combining the statistical equilibrium theory and the thermodynamics of linear irreversible processes. Generalized force and flux are defined in irreversible thermodynamics limit. The kinetic equation for the magnetization is obtained by using linear response theory. Temperature and also crystal field dependencies of the relaxation time are obtained in the vicinity of phase transition points. We found that the relaxation time exhibits divergent treatment near the order–disorder phase transition point as well as near the isolated critical point whereas it displays cusp behavior near the first-order phase transition point. In addition, much effort has been devoted to investigation of complex magnetic susceptibility response of the system to changing applied field frequencies and it is observed that the considered disordered magnetic system exhibits unusual and interesting behavior. Furthermore, dynamical mean field critical exponents for the relaxation time and complex magnetic susceptibility are calculated in order to formulate the critical behavior of the system. Finally, a comparison of our observations with those of recently published studies is represented and it is shown that there exists a qualitatively good agreement.

Regularity and chaos at critical points of first-order quantum phase transitions

We study the interplay between regular and chaotic dynamics at the critical point of a generic first-order quantum phase transition in an interacting boson model of nuclei. A classical analysis reveals a distinct behavior of the coexisting phases in a broad energy range. The dynamics is completely regular in the deformed phase and, simultaneously, strongly chaotic in the spherical phase. A quantum analysis of the spectra separates the regular states from the irregular ones, assigns them to particular phases, and discloses persisting regular rotational bands in the deformed region.

Dynamical Properties of Potts Model with Invisible States

We study dynamic behavior of Potts model with invisible states near the first-order phase transition temperature. This model is regarded as a standard model to analyse nature of phase transition. We can control the energy barrier between the ordered state and disordered state without changing the symmetry which breaks at the transition point. We focus on melting process starting from the perfect ordered state. We calculate time-dependency of the order parameter, density of invisible state, and internal energy. All of them show two-step relaxation behavior. We also analyze the relationship between the characteristic melting time and characteristic scale of the energy barrier by changing the number of invisible states. We find that characteristic melting time increases as the energy barrier enlarges in this model. This model is regarded as a fundamental model to analyze dynamic behavior near the first-order phase transition point.

Evidences of the Instability Fixed Points of First-Order Phase Transitions

We study the dynamics of the first-order phase transitions in the two-dimensional Potts model driven by a linearly varying temperature using a finite-time scaling with extended dynamic Monte Carlo renormalization group method. It is found that, for sufficiently large lattice sizes, the flows of apparent exponents of different temperature sweep rates upon renormalization show characteristics that are markedly distinct from those of continuous transitions and are argued to result from the instability fixed points involved and provide a method for estimating the associated instability exponents.

Quantum discord in the ground and thermal states of spin clusters

Quantum discord (QD) is a general measure of bipartite quantum correlations with a potential role in quantum information processing tasks. Spin clusters serve as ideal candidates for the implementation of some of the associated protocols. In this paper, we consider a symmetric spin trimer and a tetramer which describe a number of known molecular magnets and compute the QD in the ground and thermal states of the clusters. The variations of the QD as a function of an anisotropy parameter, magnetic field and temperature are investigated. We obtain a number of interesting results such as a finite value of the QD in the trimer ground state for which the pairwise entanglement is known to be zero, differences in the nature of some of the variations in the ferromagnetic and antiferromagnetic cases, and discontinuous jumps in the magnitude of the QD at first-order quantum phase transition points. A remarkable feature that is observed is that the QD completely vanishes only in the asymptotic limit of temperature T → ∞. We further study the dynamics of the QD and the pairwise entanglement at T = 0 under the effect of a dephasing channel describing the interaction of the reduced spin cluster state with independent local environments. The QD is found to vanish asymptotically as t → ∞. In the case of the spin trimer, the pairwise entanglement has a zero value at all times and reaches a zero value in a finite time in the case of the tetramer.

Phase diagram of a two-dimensional large- Q Potts model in an external field

We use a two-dimensional Wang–Landau sampling algorithm to map out the phase diagram of a Q-state Potts model with Q ⩽ 10 in an external field H that couples to one state. Finite-size scaling analyses show that for large Q the first-order phase transition point at H = 0 is in fact a triple point at which three first-order phase transition lines meet. One such line is restricted to H = 0 ; another line has H ⩽ 0 . The third line, which starts at the H = 0 triple point, ends at a critical point ( T c , H c ) which needs to be located in a two-dimensional parameter space. The critical field H c ( Q ) is positive and decreases with decreasing Q, which is in qualitative agreement with previous predictions.