Phase transitions in the Falicov–Kimball model away from half-filling

The canonical Monte Carlo method is used to study the order-disorder phase transition of the Falicov–Kimball model away from half-filling. It is shown that the transition from various inhomogeneous ground-state phases to the disordered phase can be either direct or indirect. The indirect transition means that the ground-state phase first, at critical temperature τ _c , changes to a different ordered phase and at the temperature, that can be several times higher than τ _c , finally changes to the disordered phase. It is shown that the Falicov–Kimball model, depending on the ground state phase, undergoes first order or second order phase transition or can even undergo both for the same parameters and different temperatures if the transition from the ground-state phase to the disordered phase is indirect.     

Phase transitions in the generalized spin-one-half Falicov–Kimball model in two dimensions

The extrapolation of small-cluster exact-diagonalisation calculations and the Monte-Carlo method is used to study the spin-one-half Falicov–Kimball model extended by the spin-dependent Coulomb interaction (J) between the localized f and itinerant d electrons as well as the on-site Coulomb interaction (U _ff ) between the localized f electrons. It is shown that in the symmetric case the ground-state phase diagram of the model has an extremely simple structure that consists of only two phases, and namely, the charge-density-wave (CDW) phase and the spin-density-wave (SDW) phase. The nonzero temperature studies showed that these phases persist also at finite temperatures. The critical temperature T _c for a transition from the low-temperature ordered phases to the high-temperature disordered phase is calculated numerically for various values of J and U _ff .     

Rigidity of Interfaces in the Falicov–Kimball Model

We analyze the thermodynamic properties of interfaces in the three-dimensional Falicov–Kimball model, which can be viewed as a primitive quantum lattice model of crystalline matter. In the strong coupling limit, the ionic subsystem of this model is governed by the Hamiltonian of an effective classical spin model whose leading part is the Ising Hamiltonian. We prove that the 100 interface in this model, at half-filling, is rigid, as in the three-dimensional Ising model. However, despite the above similarities with the Ising model, the thermodynamic properties of its 111 interface are very different. We prove that even though this interface is expected to be unstable for the Ising model, it is stable for the Falicov–Kimball model at sufficiently low temperatures. This rigidity results from a phenomenon of ground-state selection and is a consequence of the Fermi statistics of the electrons in the model.     

On Quantum Phase Transition. II. The Falicov–Kimball Model

The Falicov–Kimball (FK) model⁽¹⁾ involves two types of interacting particles: first the itinerant spinless electrons are quantum particles, secondly the static ions are classical particles. It is striking to see that, despite the simplicity of its hamiltonian, the phase diagram of the FK model is highly sophisticated, moreover it remains in great part conjectural. An antiferromagnetic phase transition was proven for the FK model on a square lattice in the seminal paper of T. Kennedy and E. Lieb.⁽²⁾ This result was extended by Lebowitz and Macris⁽³⁾ to small magnetic field. Then the same result was obtained by using a new method.⁽⁴⁾ The main results of this paper concerns the two dimensional FK model on a square lattice, for which we apply the general results contained in ref. 5. First there exists an effective hamiltonian which is a long range many body Ising model, and which governs the behaviour of the ions. Secondly we compute explicitly the truncated effective hamiltonian up to the fourth order w.r.t. a small parameter (the inverse of the on site energy). Finally we use the classical Pirogov–Sinai theory, to get the hierarchy of the phase diagrams up to the fourth order. More precisely, we show that, when the chemical potential varies, the FK model exhibits, at low temperature, a sequence of phase transitions: first between phases of period two, then of period three, then of period four, and finally of period five. In each case the completeness of the phase diagram is proved. This paper supports the conjecture that the phase diagram of the FK model contains periodic phases outside of a Cantor set.     

Periodic Ground States in the Neutral Falicov–Kimball Model in Two Dimensions

We consider the Falicov–Kimball model in two dimensions in the neutral case, i.e., the number of mobile electrons is equal to the number of ions. For rational densities between 1/3 and 2/5 we prove that the ground state is periodic if the strength of the attraction between the ions and electrons is large enough. The periodic ground state is given by taking the one dimensional periodic ground state found by Lemberger and then extending it into two dimensions in such a way that the configuration is constant along lines at a 45 degree angle to the lattice directions.     

Ground State Properties¶of the Neutral Falicov–Kimball Model

We determine the large U ground states in the neutral two-dimensional Falicov-Kimball model for a sequence of densities converging to 0. For rational densities in (1/6,2/11) we show that the ground states exhibit a phase separation.     

The possibility of detection of finite temperature stripe ordering in 2D spinless Falicov–Kimball model

This paper announces a possibility of detection of finite-temperature stripe ordering in the two-dimensional Falicov–Kimball model at half-filling by extensive Monte Carlo simulations. Moreover, the tools to study orderings and to detect phase transition temperatures are presented. The use of Binder's cumulant is supplemented by finite-size magnetization profiles not analyzed previously in this context. Continuous character of phase transitions is announced. Analyses proving the existence of more complicated phases of finite-temperature stripe ordering than the checkerboard one conclude the paper.     

Phase transitions in shape memory alloys: A non-isothermal Ginzburg–Landau model

We propose a model to describe non-isothermal transitions from the austenite to the martensite phase occurring in shape memory materials. The phenomenon is set in the context of the Ginzburg–Landau theory of phase transitions, postulating a free energy depending on the temperature, the stress and the order parameter. In the one-dimensional case, when only two martensitic variants are involved and stress and deformation have a fixed direction, our choice of free energy allows us to deduce a phase diagram describing the main features of a typical SMA. The Ginzburg–Landau equation ruling the evolution of the order parameter is coupled with the equations of thermoelasticity by assuming a constitutive equation relating stress, strain and order parameter. The consistency of the model with the second law of Thermodynamics in the form of the Clausius–Duhem inequality is proved. Finally a possible generalization to a three-dimensional model is proposed, by introducing a tensor-valued order parameter.     

Inverse transitions in the Ghatak–Sherrington model with bimodal random fields

The present work studies the Ghatak–Sherrington (GS) model in the presence of a longitudinal magnetic random field (RF) _hi$h_i$ following a bimodal distribution. The model considers a random bond interaction _Ji,j$J_{i,j}$ which follows a Gaussian distribution with mean _J0/N$J_0/N$ and variance J²/N$J^2/N$. This allows us to introduce the bond disorder strength parameter J/_J0$J/J_0$ to probe the combined effects of disorder coming from the random bond and the discrete RF over unusual phase transitions known as inverse transitions (ITs). The results within a mean field approximation indicate that these two types of disorder have completely distinct roles for the ITs. They indicate that bond disorder creates the necessary conditions for the presence of inverse freezing, or even inverse melting, depending on the bond disorder strength, while the RF tends to enforce mechanisms that destroy the ITs.     

Nonlocal Coulomb interaction in the two-dimensional spin-<Emphasis Type="Bold">1/2</Emphasis> Falicov–Kimball model

The two-dimensional (2D) extended Falicov–Kimball model has been studied to observe the role of nonlocal Coulomb interaction (U _nc) using an exact diagonalization technique. The f-state occupation (n ^f ), the f–d intersite correlation function (c _fd), the specific heat (C), entropy (S) and the specific heat coefficient (γ) have been examined. Nonlocal Coulomb interaction-induced discontinuous insulator-to-metal transition occurs at a critical f-level energy. More ordered state is obtained with the increase of U _nc. In the specific heat curves, two-peak structure as well as a single-peak structure appears. At low-temperature region, a sharp rise in the specific heat coefficient γ is observed. The peak value of γ shifts to the higher temperature region with U _nc.     

Phase transitions in CuS–Ag2S nanoparticle system

(Ag₂)_xCu_1?xS, x = .2, .4, .6 and .8 nanoparticles were synthesized by the solvothermal method. The as-synthesized nanoparticles were characterized by X-ray diffraction to study the crystal structure and size. The surface morphologies of the above samples were studied using scanning electron microscope. As there is continuous shift in the lower wavelength absorption edge of the UV–VIS spectrum of these samples with concentration, (Ag₂)_xCu_1?xS nanoparticles can be tuned to different band gap energies by varying the composition. The D.C. electrical resistance was measured in the temperature range 310–485 K. As Ag₂S transforms from monoclinic to bcc at around 450 K, copper sulfide nanoparticles also shows a phase transition at around 470 K, the effects of these two transitions are seen in the resistance measurements and in the UV–VIS spectra of the entire system. The electrical resistance of (Ag₂)_xCu_1?xS nanoparticles rapidly reduces as more and more copper sulfide is added.     

Phase transitions in a holographic s $$$$ p model with back-reaction

In a previous paper (Nie et al. in JHEP 1311:087, arXiv:1309.2204 [hep-th], 2013), we presented a holographic s \(+\) p superconductor model with a scalar triplet charged under an SU(2) gauge field in the bulk. We also study the competition and coexistence of the s-wave and p-wave orders in the probe limit. In this work we continue to study the model by considering the full back-reaction. The model shows a rich phase structure and various condensate behaviors such as the “n-type” and “u-type” ones, which are also known as reentrant phase transitions in condensed matter physics. The phase transitions to the p-wave phase or s \(+\) p coexisting phase become first order in strong back-reaction cases. In these first order phase transitions, the free energy curve always forms a swallow tail shape, in which the unstable s \(+\) p solution can also play an important role. The phase diagrams of this model are given in terms of the dimension of the scalar order and the temperature in the cases of eight different values of the back-reaction parameter, which show that the region for the s \(+\) p coexisting phase is enlarged with a small or medium back-reaction parameter but is reduced in the strong back-reaction cases.     

Phase transitions in low-dimensional ψ 4 systems

The phase transition in a planar array of weakly coupled Ginzburg–Landau chains with real order parameter is studied, using an original variant of the two-level approximation. The results are extended to the quantum phase transition in a chain of quantum double well oscillators, coupled with an elastic interaction, using the matrix transfer method.     

Phase transitions in “small” systems

Traditionally, phase transitions are defined in the thermodynamic limit only. We discuss how phase transitions of first order (with phase separation and surface tension), continuous transitions and (multi)-critical points can be seen and classified for small systems. “Small” systems are systems where the linear dimension is of the characteristic range of the interaction between the particles; i.e. also astrophysical systems are “small” in this sense. Boltzmann defines the entropy as the logarithm of the area of the surface in the mechanical N-body phase space at total energy E. The topology of S(E,N) or more precisely, of the curvature determinant allows the classification of phase transitions without taking the thermodynamic limit. Micro-canonical thermo-statistics and phase transitions will be discussed here for a system coupled by short range forces in another situation where entropy is not extensive. The first calculation of the entire entropy surface S(E,N) for the diluted Potts model (ordinary (q=3)-Potts model plus vacancies) on a square lattice is shown. The regions in {E,N} where D>0 correspond to pure phases, ordered resp. disordered, and D<0 represent transitions of first order with phase separation and “surface tension”. These regions are bordered by a line with D=0. A line of continuous transitions starts at the critical point of the ordinary (q=3)-Potts model and runs down to a branching point P_m. Along this line vanishes in the direction of the eigenvector of D with the largest eigen-value . It characterizes a maximum of the largest eigenvalue . This corresponds to a critical line where the transition is continuous and the surface tension disappears. Here the neighboring phases are indistinguishable. The region where two or more lines with D=0 cross is the region of the (multi)-critical point. The micro-canonical ensemble allows to put these phenomena entirely on the level of mechanics. Received 18 October 1999 and received in final form 17 November 1999     

Tricritical point in quantum phase transitions of the Coleman–Weinberg model at Higgs mass

The tricritical point, which separates first and second order phase transitions in three-dimensional superconductors, is studied in the four-dimensional Coleman–Weinberg model, and the similarities as well as the differences with respect to the three-dimensional result are exhibited. The position of the tricritical point in the Coleman–Weinberg model is derived and found to be in agreement with the Thomas–Fermi approximation in the three-dimensional Ginzburg–Landau theory. From this we deduce a special role of the tricritical point for the Standard Model Higgs sector in the scope of the latest experimental results, which suggests the unexpected relevance of tricritical behavior in the electroweak interactions.     

Pre-equilibrium γ rays from single-particle radiative transitions in the hybrid model

A formulation is developed for γ ray emission via single-particle radiative transitions in the hybrid model. Pre-equilibrium γ emission rates, derived using the Brink-Axel hypothesis and detailed balance, are influenced little by the dipole effective charge and are consistent with the established equilibrium limit. The model can explain a considerable part of the γ rays in the giant resonance range observed in nuclear reactions.     

Phase transitions in h-thiourea under electric‐field

Abstract

Dielectric constant, spontaneous polarization and pyroelectric response measurements were performed on thin samples (e < 100 μm) of H-thiourea as a function of temperature and applied electric field. Along with previous data obtained by optical birefringence, X-ray and neutron diffraction techniques, the results put in evidence three features in the modulated region between the ferroelectric state and the paraelectric one. The tricritical point is determined for E_tr ? 2075 V/mm and T_tr ? 192 K.     

Entanglement for two-atom Tavis–Cummings model with degenerate two-photon transitions in the presence of the Stark shift

The dynamics of atom–field entanglement for two two-level atoms with degenerate two-photon transitions interacting with one-mode radiation field with taking into account the Stark shift is investigated. Asymptotic solutions for system state vectors are obtained in the approximation of large initial coherent fields. The atom–field entanglement is investigated also on the basis of the linear atomic entropy dynamics. The possibility of the system being initially in a pure disentangled state to revive into this state during the evolution process is shown. Conditions and times of disentanglement are derived.     

Phase transitions in a hydrogen-rich compound：tetramethylsilane

High-pressure behavior of tetramethylsilane is investigated by synchrotron powder X-ray diffraction and Raman scattering at pressures up to 30 GPa and room temperature. Our results reveal the analogous phase transitions, though slight hysteresis for the certain phases. A new phase is found to appear at 4.2 GPa due to the disappeared Raman mode. These findings offer the possibility to understand the evolution of the H-H bonding with pressure in such hydrogen-rich compounds.