First-order Transition Point Research Articles

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.

Hexagonal Type Ising Nanowire with Spin-1 Core and Spin-2 Shell Structure

Thermodynamic properties and phase diagrams of a mixed spin-(1,2) Ising ferrimagnetic system with single ion anisotropy on hexagonal nanowire are studied by using effective-field theory with correlations. The susceptibility, internal energy and specific heat of the system are numerically examined and some interesting phenomena in these quantities are found. The effect of the Hamiltonian parameters on phase diagrams are examined in detail. Besides second-order phase transition, lines of first-order transition and tricritical points are found. In particular, we found that for some negative values of single-ion anisotropies, there exist first-order phase transitions.

Cubic-quintic nonlinearity in superfluid Bose-Bose mixtures in optical lattices: Heavy solitary waves, barrier-induced criticality, and current-phase relations

We study superfluid (SF) states of strongly interacting Bose-Bose mixtures with equal mass and intra-component interaction in optical lattices both in the presence and absence of a barrier potential (BP). We show that the SF order parameters obey the two-component nonlinear Schroedinger equation (NLSE) with not only cubic but also quintic nonlinearity in the vicinity of the first-order transitions to the Mott insulators with even fillings. In the case of no BP, we analyze solitary-wave (SW) solutions of the cubic-quintic NLSE. When the SF state changes from a ground state to a metastable one, a standard dark SW turns into a bubble-like dark SW, which has a non-vanishing density dip and no pi phase kink even in the case of a standing SW. It is shown that the former and latter SW are dynamically unstable against an out-of-phase fluctuation and an in-phase fluctuation, respectively, and the dynamical instabilities are weakened when one approaches the transition point. We find that the size and the inertial mass of the SW diverge at the first-order transition point. We suggest that the divergence of the inertial mass may be detected through measurement of the relation between the velocity and the phase jump of the SW. In the presence of BP, we reveal that when the barrier strength exceeds a certain critical value, the SF state that was metastable without the barrier is destabilized towards complete disjunction of the SF. The presence of the critical BP strength indicates that the strong BP qualitatively changes the criticality near the metastability limit of the SF state. We derive critical behaviors of the density, the compressibility, and the critical current near the metastability limit induced by the BP. It is also found that the relation between the supercurrent and the phase jump across the BP exhibits a peculiar behavior, owing to the non-topological nature of the bubble-like SW.

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.

First-order and tricritical wetting transitions in the two-dimensional Ising model caused by interfacial pinning at a defect line.

We present a study of the critical behavior of the Blume-Capel model with three spin states (S=±1,0) confined between parallel walls separated by a distance L where competitive surface magnetic fields act. By properly choosing the crystal field (D), which regulates the density of nonmagnetic species (S=0), such that those impurities are excluded from the bulk (where D=-∞) except in the middle of the sample [where D(M)(L/2)≠-∞], we are able to control the presence of a defect line in the middle of the sample and study its influence on the interface between domains of different spin orientations. So essentially we study an Ising model with a defect line but, unlike previous work where defect lines in Ising models were defined via weakened bonds, in the present case the defect line is due to mobile vacancies and hence involves additional entropy. In this way, by drawing phase diagrams, i.e., plots of the wetting critical temperature (T(w)) versus the magnitude of the crystal field at the middle of the sample (D(M)), we observe curves of (first-) second-order wetting transitions for (small) high values of D(M). Theses lines meet in tricritical wetting points, i.e., (T(w)(tc),D(M)(tc)), which also depend on the magnitude of the surface magnetic fields. It is found that second-order wetting transitions satisfy the scaling theory for short-range interactions, while first-order ones do not exhibit hysteresis, provided that small samples are used, since fluctuations wash out hysteretic effects. Since hysteresis is observed in large samples, we performed extensive thermodynamic integrations in order to accurately locate the first-order transition points, and a rather good agreement is found by comparing such results with those obtained just by observing the jump of the order parameter in small samples.

Nonequilibrium first-order phase transition in coupled oscillator systems with inertia and noise.

We study the dynamics of a system of coupled oscillators of distributed natural frequencies, by including the features of both thermal noise, parametrized by a temperature, and inertial terms, parametrized by a moment of inertia. For a general unimodal frequency distribution, we report here the complete phase diagram of the model in the space of dimensionless moment of inertia, temperature, and width of the frequency distribution. We demonstrate that the system undergoes a nonequilibrium first-order phase transition from a synchronized phase at low parameter values to an incoherent phase at high values. We provide strong numerical evidence for the existence of both the synchronized and the incoherent phase, treating the latter analytically to obtain the corresponding linear stability threshold that bounds the first-order transition point from below. In the limit of zero noise and inertia, when the dynamics reduces to the one of the Kuramoto model, we recover the associated known continuous transition. At finite noise and inertia but in the absence of natural frequencies, the dynamics becomes that of a well-studied model of long-range interactions, the Hamiltonian mean-field model. Close to the first-order phase transition, we show that the escape time out of metastable states scales exponentially with the number of oscillators, which we explain to be stemming from the long-range nature of the interaction between the oscillators.

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.

The t-J model of hard-core bosons in slave-particle representation and its Monte-Carlo simulations

We study the system of hard-core bosons (HCB) with two species in the three-dimensional lattice at finite temperatures. In the strong-correlation limit, the system becomes the bosonic t-J model, that is, the t-J model of “bosonic electrons”. The bosonic “electron” operator Bxσ at the site x with a two-component spin σ(= 1, 2***) is treated as a HCB operator, and represented by a composite of two slave particles; a spinon described by a Schwinger boson (CP1 boson) zxσ and a holon described by a HCB field φx as Bxσ = φ†xzxσ.*** This φx is again represented by another CP1 quasi-spinon operator ωxa*** (a = 1, 2***). The phase diagrams of the resulting double CP1 system obtained by Monte Carlo simulations involve first-order and second-order phase boundaries. We present in detail the techniques and algorithm to reduce the hysteresis and locate the first-order transition points.

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.

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.

Phase Front Near the Critical End Point as the Boundary of the Polar Nanoregions in Relaxor Ferroelectrics

The static modulation structure of the phase front at the field-induced first-order transition point near the critical end point (CEP) was discussed on the basis of the Landau-type free-energy function. It was confirmed that the field E dependence of the thickness of the phase front is proportional to ( E CEP - E ) -1/2 , diverging at CEP ( E = E CEP ). It is pointed out that, in relaxor ferroelectrics, the boundary between the polar nanoregion (PNR) and the paraelectric matrix may be considered as a phase front, and that the contribution to the dielectric response of the phase front cannot be ignored.

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.

Thermodynamic geometry of the Garfinkle–Horowitz–Strominger dilaton black hole

This paper studies the thermodynamic properties of the Garfinkle–Horowitz–Strominger dilaton black hole from the viewpoint of geometry. It calculates the heat capacity and the temperature of the black hole, Weinhold metric and Ruppeiner metric are also obtained respectively. It finds that they are both curved and the scalar curvature of the Weinhold geometry consists with the first-order transition point reproduced from the capacity, while the Ruppeiner one is both in accordance with the first-order and the second-order phase transition points reproduced from the capacity.

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.

Mean-field and Monte Carlo studies of a mixed spin-1 and spin-2 Ising system with different anisotropies

The magnetic properties of a mixed spin-1 and spin-2 Ising ferromagnetic system with different anisotropies are studied by mean field theory (MFT) and the Monte Carlo method (MC). The dependence of the phase diagram on single-ion anisotropy strengths is studied by MFT. Besides second-order phase transition, lines of first-order transition and tricritical points are found. In particular, we found that the system under study may exhibit reentrant phenomenon. The Monte Carlo method is then employed to validate the reentrant phenomenon on simple cubic lattice, which cannot be found in spin-1 and spin-3/2 counterpart using this method.(c) 2006 American Institute of Physics.

Finite-temperature Mott transitions in the multiorbital Hubbard model

We investigate the Mott transitions in the multi-orbital Hubbard model at half-filling by means of the self-energy functional approach. The phase diagrams are obtained at finite temperatures for the Hubbard model with up to four-fold degenerate bands. We discuss how the first-order Mott transition points $U_{c1}$ and $U_{c2}$ as well as the critical temperature $T_c$ depend on the orbital degeneracy. It is elucidated that enhanced orbital fluctuations play a key role to control the Mott transitions in the multi-orbital Hubbard model.

Scaling and Goldstone effects in a QCD with two flavours of adjoint quarks

We study QCD with two Dirac fermions in the adjoint representation at finite temperature by Monte Carlo simulations. In such a theory the deconfinement and chiral phase transitions occur at different temperatures. We locate the second-order chiral transition point at β c = 5.624 ( 2 ) and show that the scaling behaviour of the chiral condensate in the vicinity of β c is in full agreement with that of the 3d O ( 2 ) universality class, and to a smaller extent comparable to the 3d O ( 6 ) class. From the previously determined first-order deconfinement transition point β d = 5.236 ( 3 ) and the two-loop beta function we find the ratio T c / T d ≈ 7.8 ( 2 ) . In the region between the two phase transitions we explicitly confirm the quark mass dependence of the chiral condensate which is expected due to the existence of Goldstone modes like in 3d O ( N ) spin models. At the deconfinement transition 〈 ψ ¯ ψ 〉 shows a gap, and below β d , it is nearly mass-independent for fixed β.

A Monte Carlo study of the first-order transition in a Heisenberg FCC antiferromagnet

Nearest-neighbor Heisenberg antiferromagnet on a face-centered cubic lattice is studied by extensive Monte Carlo simulations in zero magnetic field. The parallel tempering algorithm is utilized, which allows to overcome a slow relaxation of the magnetic order parameter and fully equilibrate moderate size clusters with up to N ~ 7*10^3 spins. By collecting energy and order parameter histograms on clusters with up to N ~ 2*10^4 sites we accurately locate the first-order transition point at T_c=0.4459(1)J.

Static and dynamic properties of the XXZ chain with long-range interactions

The one-dimensional XXZ model ( s = 1 2 ) in a transverse field, with uniform long-range interactions among the transverse components of the spins, is studied. The model is exactly solved by introducing the Jordan–Wigner transformation and the integral Gaussian transformation. The complete critical behaviour and the critical surface for the quantum and classical transitions, in the space generated by the transverse field and the interaction parameters, are presented. The crossover lines for the various classical/quantum regimes are also determined exactly. It is shown that, besides the tricritical point associated with the classical transition, there are also two quantum critical points: a bicritical point where the classical second-order critical line meets the quantum critical line, and a first-order transition point at zero field. It is also shown that the phase diagram for the first-order classical/quantum transitions presents the same structure as for the second-order classical/quantum transitions. The critical classical and quantum exponents are determined, and the internal energy, the specific heat and the isothermal susceptibility, χ T zz , are presented for the different critical regimes. The two-spin static and dynamic correlation functions, 〈 S j z S l z 〉 , are also presented, and the dynamic susceptibility, χ q zz ( ω ) , is obtained in closed form. Explicit results are presented at T = 0 , and it is shown that the isothermal susceptibility, χ T zz , is different from the static one, χ q zz ( 0 ) . Finally, it is shown that, at T = 0 , the internal energy close to the first-order quantum transition satisfies the scaling form recently proposed by Continentino and Ferreira.

Multifractal analysis of weak Gibbs measures and phase transition—application to some Bernoulli convolutions

For a given expanding d-fold covering transformation of the one-dimensional torus, the notion of weak Gibbs measure is defined by a natural generalization of the classical Gibbs property. For these measures, we prove that the singularity spectrum and the L q -spectrum form a Legendre transform pair. The main difficulty comes from the possible existence of first-order phase transition points, that is, points where the L q -spectrum is not differentiable. We give examples of weak Gibbs measure with phase