Mean-field theory for quenched reduced large-N gauge model

The reduced model à la Eguchi and Kawai, its quenched version and the Wilson theory in the string variable representation are studied by employing the loop expansion around the mean field. The spontaneous breakdown of the U(1)^d symmetry in the Eguchi-Kawai model is thoroughly investigated. It is shown that the quenched reduced model undergoes the first-order phase transition in excellent agreement with the Monte Carlo data. The quenched reduced model is shown to be equivalent to the standard Wilson theory by comparing with the string variable Wilson theory at any finite order in the loop expansion in the large-N limit.     

An improved mean field approach to the phase structure in ZN gauge theory in four dimensions

We extend the mean field approximation scheme to include the effect of fluctuation of the gauge field. As a consequence, we successfully obtain for the Z_N theory (N > 5) the phase transition which separates the Coulomb phase from the ordered phase, as well as that separating the Coulomb and disordered phases. The former transition shows characteristics of higher-order phase transitions.     

Determination of the phase structure of the four-dimensional coupled gauge-Higgs Potts model

Using Monte Carlo simulations the phase structure of the four-dimensional N-state gauge Potts model coupled to Higgs fields is determined. A three-phase diagram is established. In the Z(2) case, a first and a second-order transition lines are present. For Z(5) and Z(10) only first-order transition lines appear. The results are consistent with previous mean field predictions.     

Dynamics and thermodynamics of rotators interacting with both long- and short-range couplings

The effect of nearest-neighbor coupling on the thermodynamic and dynamical properties of the ferromagnetic Hamiltonian mean field model (HMF) is studied. For a range of antiferromagnetic nearest-neighbor coupling, a canonical first-order transition is observed, and the canonical and microcanonical ensembles are non-equivalent. In studying the relaxation time of non-equilibrium states it is found that as in the HMF model, a class of non-magnetic states is quasi-stationary, with an algebraic divergence of their lifetime with the number of degrees of freedom N. The lifetime of metastable states is found to increase exponentially with N as expected.     

Random source induced spontaneous symmetry breaking in scalar field theories

We study the effective potential for scalar field theories in the presence of gaussian random sources, coupled to the scalar field in a self-consistent way. We compute the effective potential both in the loop and in the 1/N expansions and find various instabilities. The only feasible instabilities are the ones induced by (formally) imaginary random sources. The pertinent phase transition is a first-order transition.     

Statistical properties of random environment of 1<Emphasis Type="Italic">D</Emphasis> quantum <Emphasis Type="Italic">N</Emphasis>-particles system in external field

The investigation of 1D quantum N-particle system (PS) with relaxation in the random environment under the influence of external field is conducted within the framework of the stochastic differential equation of the Langevin—Schrödinger (L—Sch) type. Using L—Sch equation, the 2D second-order nonstationary partial differential equation is found, which describes the quantum distribution in the environment, depending on the energy of nonperturbed 1D quantum N-PS and on the external field parameters. It is shown that the average value of the interaction potential between 1D disordered quantum N-PS and the external field, has the ultraviolet divergence. This problem is solved by the renormalization of the equation for the function of quantum distribution. It is shown that it has a sense of dimensional renormalization which is characteristic for the quantum field theory. Critical properties of the environment are investigated in detail. The possibility of the first-order phase transition in the environment distribution depending on amplitude of an external field is been shown.     

Critical behaviors of bond and crystal field dilution Blume–Emery–Griffiths model

The critical behavior of the spin-1 bond and crystal field dilution Blume–Emery–Griffiths model have been investigated on simple-cubic lattice within the framework of the effective field theory. In particular, both bond dilution and random crystal field are considered at the same time. The interplay between bond and crystal field dilution constructs rich and interesting phase diagrams. Significant distinctions are exhibited. When positive ratio α changes in a certain range, there exist double tricritical points in phase-transition lines in T–D plane. Moreover, this first-order phase transition is enlarged with increasing of ratio α at a fixed crystal field dilution concentration, while this first-order phase transition will shrink when bond dilution concentration is fixed. In addition, we observe that there exist two bond percolation thresholds for negative crystal field and α>0 in T–P plane.     

Asymmetric <Emphasis Type="Italic">c</Emphasis>(4×4) → γ(2×4) reconstruction phase transition on the (001)GaAs surface

The c(4×4) → γ(2×4) reconstruction phase transition on the (001)GaAs surface is studied experimentally. It is shown that it is a first-order phase transition. The phase transition is found to exhibit a highly asymmetric hysteresis. The difference between the direct and inverse runs of the hysteresis is explained in terms of the mean field theory of an adsorption-induced phase transition by the substantial contribution of lateral multiparticle interactions in the adsorbate.     

Gaussian fluctuations to U(N) and SU(N) lattice gauge theories in the mean field approximation

The mean field can be considered as a classical solution of an appropriately reformulated version of lattice gauge theories. Axial gauge fixing renders it stable. The quadratic forms for the fluctuations in the gaussian approximation are analyzed. The gaussian correction to the mean field free energy is expressed for all U(N) and SU(N) in terms of structure functions that are explicitly calculated for U(N), SU(∞, and SU(∞) numerical calculations are performed for the phase transition point, its latent heat, and some correlation lengths that are characteristic for this kind of mean field approach.     

Mean field solution to the intermediate valence problem

We introduce a mean field theory of IV systems, corresponding to the limit of infinite degeneracy N = 2j + 1. For a single RE impurity we correct it to next order in 1/N. For the lattice the mean field theory for the first time leads to an ab initio derivation of a renormalized band structure.     

The quark-nucleon phase diagram and quantum chromodynamics

The temperature dependence of a conjectured first-order phase transition between nuclear matter and quark-gluon matter is calculated for temperatures below T = 200 MeV. On the nuclear side a rather successful meson-nucleon mean field theory is applied while quark-gluon matter at large densities and finite temperatures is described perturbatively by quantum chromodynamics. Outside the finite volume of hot and dense quark-gluon matter the physical vacuum is characterized, by the newly determined bag parameter Λ_B = 235 MeV. We observe a dramatic drop in the density of nuclear matter at the phase transition point as the temperature increases, if the scale parameter Λ of QCD is chosen as Λ = 100 MeV. For larger values of Λ the effect is less pronounced. Further work is required to settle this problem.     

Ground-state phase diagrams of Ising metamagnet in a mixed longitudinal and transverse magnetic field

The ground-state magnetic properties of a two-sublattice Ising metamagnet in a mixed longitudinal and transverse magnetic field are studied within the effective-field theory. A parameter j₂=J₂/J₁ is introduced, which reflects the strength ratio of spin coupling between adjacent planes and in each plane. In addition to the second-order transition lines, the first-order transition lines are also presented, since the ground-state energy can be calculated numerically. The ground-state phase diagrams in h_x–h_z are presented. The results show that when j₂<0 the phase transition of the system is always first-order for h_x<2.751, and when −1000?j₂<0 it is always second-order for h_x>4.36. For the given h_x (0<h_x<14.71), the longitudinal critical magnetic field increases as j₂ decreases. The reentrant phenomenon occurs in the range of j₂<−11.89, h_x>14.71. There is no fourth-order critical point in the phase diagrams given by using EFT as found by using mean field theory (MFT).     

Effective scalar field theory for the electroweak phase transition

We investigate an effective model for the finite-temperature symmetry-restoration phase transition of the electroweak theory. It is obtained by dimensional reduction of the (3 + 1)-dimensional full theory and by subsequent integration over all static gauge degrees of freedom. The resulting theory corresponds to a 3-dimensional O(4) ferromagnet containing cubic and quartic terms of the field in its potential function. Possible nonperturbative effects of a magnetic screening mass are parametrically included in the potential. We analyse the theory using mean-field and numerical Monte Carlo (MC) simulation methods. At the value of the physical Higgs mass, m_H = 37 GeV, considered in the present investigation, we find a discontinuous symmetry-restoring phase transition. We determine the critical temperature, order parameter jump, interface tension and latent heat characteristics of the transition. The Monte Carlo results indicate a somewhat weaker first-order phase transition as compared to the mean-field treatment, demonstrating that non-perturbative fluctuations of the Higgs field are relevant. This effect is especially important for the interface tension. Any observation of hard first-order transition could result only from non-perturbative effects related to the gauge degrees of freedom.     

Equilibrium properties of a spin-1 Ising system with bilinear,biquadratic and odd interactions

The equilibrium properties of the spin-1 Ising system Hamiltonian with arbitrary bilinear (J), biquadratic (K) and odd (L), which is also called dipolar-quadrupolar, interactions is studied for zero magnetic field in the lowest approximation of the cluster variation method. The odd interaction is combined with the bilinear (dipolar) and biquadratic (quadrupolar) exchange interactions by the geometric mean. In this system, phase transitions depend on the ratio of the coupling parameters, α = J/K; therefore, the dependence of the nature of the phase transition on α is investigated extensively and it is found that for α ⩽ 1 and α ⩾ 2000 a second-order phase transition occurs, and for 1 < α < 2000 a first-order phase transition occurs. The critical temperatures in the case of a second-order phase transition and the upper and lower limits of stability temperature in the case of a first-order phase transition are obtained for different values of α calculated using the Hessian determinant. The first-order phase transition temperatures are found by using the free energy values while increasing and decreasing the temperature. Besides the stable branches of the order parameters, we establish also the metastable and unstable parts of these curves and the thermal variations of these solutions as a function of the reduced temperature are investigated. The unstable solutions for the first-order phase transitions are obtained by displaying the free energy surfaces in the form of a contour map. Results are compared with the spin-1 Ising system Hamiltonian with the bilinear and biquadratic interactions and it is found that the odd interaction greatly influences the phase transitions.     

Nonlocal PNJL model beyond mean field

A nonlocal chiral quark model is consistently extended beyond mean field using a strict 1/N _c expansion scheme. It is found that the 1/N _c corrections lead to a lowering of the temperature of the chiral phase transition in comparison with the mean-field result. On the other hand, near the phase transition the 1/N _c expansion breaks down and a nonperturbative scheme for the inclusion of mesonic correlations is needed in order to describe the phase transition region.     

Magnetic properties of Ising metamagnet in both external longitudinal and transverse fields

The phase diagrams of a two-sublattice Ising metamagnet at finite temperature in a mixed longitudinal field and a transverse magnetic field are investigated by the use of an effective-field theory (EFT) with correlations. In addition to the second-order transition lines, the first-order transition lines are also presented in the phase diagrams, since the Gibbs free energy can be calculated numerically. The results show that there is no fourth-order critical line in the phase diagrams given by using EFT as found by using mean-field theory (MFT). The tricritical lines and their projection in the t−h_x plane obtained by using EFT are also quite different from those by using MFT. Only one type of phase diagram is obtained by using EFT while three kinds of phase diagrams are obtained by using MFT, which indicates that only the first kind of phase diagrams obtained by using MFT is reliable. Furthermore, it is shown that the region of first-order transitions increases as the transverse magnetic field h_x decreases.     

First-order transitions from singly peaked distributions

Suppose that, in the thermodynamic limit, a single-component particle system exhibits a standard first-order transition marked by a jump in the density, ρ, at a chemical potential μ_σ(T). In grand canonical simulations of model fluids that realize such a transition when L→∞ (where L is the linear dimension of the simulation volume) the presence of the transition is typically signaled by the appearance of a double-peaked structure in the distribution function, P_N(T,μ_σ;L), of the particle number, N. A simple, explicit counterexample is presented, however, that proves, contrary to popular beliefs, that the converse proposition is false: i.e., a single-peaked distribution, P_N(T,μ_σ;L), may, when L→∞, give rise to a first-order transition. Alternatively, the existence of a first-order transition does not imply a double-peaked distribution. Systems that may exhibit such single-peaked, first-order behavior are discussed and a possible route to constructing explicit models exhibiting the phenomenon is described. Strategies to use in simulating such systems are briefly considered in the light of related studies.     

Phase diagram of the Ising antiferromagnet with nearest-neighbor and next-nearest-neighbor interactions on a square lattice

The phase diagram of the Ising model in the presence of nearest-neighbor (J₁) and next-nearest-neighbor (J₂) interactions on a square lattice is studied within the framework of the differential operator technique. The Hamiltonian is solved by effective-field theory in finite cluster (we have chosen N=4 spins). We have proposed a functional for the free energy (similar to Landau expansion) to obtain the phase diagram in the (T,α) space (α=J₂/J₁), where the transition line from the superantiferromagnetic (SAF) to the paramagnetic (P) phase is of first-order in the range 1/2<α<0.95 in contrast to previous study of CVM (Cluster Variational Method) that predict first-order transition for α=1.0. Our results for α=1.0 are in accordance with MC (Monte Carlo) simulations, that predict a second-order transition.     

Magnetic ordering in uranium monophosphide

The magnetic ordering in uranium monophosphide (UP) has been studied by neutron diffraction from a single crystal in a magnetic field. UP orders at T_N ? 122 ± 0.1 K with the type-I antiferromagnetic structure (+-+-), the ordering taking place in a first-order transition. At T₀ = 22.5 K the ordered magnetic moment jumps from 1.7 μ_B to 1.9 μ_B. With a magnetic field H = 25 kOe applied along the [11&#x0304;10] direction, it is found that UP has the collinear single-$\text{K}$ type-I structure above T₀ and undergoes a first-order transition to the planar double-$\text{K}$ type-I structure, accompanied by a “moment jump” due to the change in the moment direction from <001> to <110>.