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.     

Spectral–Dynamic Model of the Hot Plasma Layer Expansion

Journal of Experimental and Theoretical Physics - We propose a theoretical model describing the expansion of a plasma layer into vacuum for an arbitrary electron plasma component temperature....     

Instability of Non—Fermi Liquid Behavior in the Two—Channel Kondo Model

The effects of interchannel scattering of conduction electrons by the impurity and repulsion of conduction electrons at the impurity site on the two-channel Kondo model are simultaneously considered in this paper,It is shown that these two perturbations will substantially modify the usual local non-Fermi liquid behavior of the two-channel Kondo model.With bosonization and unitary transformations we find that the system can be transformed into a single channel Kondo model with anisotropy between longitudinal and transverse exchange couplings,Whatever for originally antiferromagnetic or ferromagnetic isotropic coupling,the system always flows to strong-coupling limit,which exhibits local Fermi liquid behavior at low temperatures.     

Critical Hardy–Lieb–Thirring Inequalities for Fourth-Order Operators in Low Dimensions

This paper considers Hardy–Lieb–Thirring inequalities for higher order differential operators. A result for general fourth-order operators on the half-line is developed, and the trace inequality

Superintegrability in Two Dimensions and the Racah–Wilson Algebra

The analysis of the most general second-order superintegrable system in two dimensions: the generic 3-parameter model on the 2-sphere is cast in the framework of the Racah problem for the \({\mathfrak{su}(1,1)}\) algebra. The Hamiltonian of the 3-parameter system and the generators of its quadratic symmetry algebra are seen to correspond to the total and intermediate Casimir operators of the combination of three \({\mathfrak{su}(1,1)}\) algebras, respectively. The construction makes explicit the isomorphism between the Racah–Wilson algebra, which is the fundamental algebraic structure behind the Racah problem for \({\mathfrak{su}(1, 1)}\) , and the invariance algebra of the generic 3-parameter system. It also provides an explanation for the occurrence of the Racah polynomials as overlap coefficients in this context. The irreducible representations of the Racah–Wilson algebra are reviewed as well as their connection with the Askey scheme of classical orthogonal polynomials.     

Singular Dimensions of the¶N= 2 Superconformal Algebras. I

Verma modules of superconfomal algebras can have singular vector spaces with dimensions greater than 1. Following a method developed for the Virasoro algebra by Kent, we introduce the concept of adapted orderings on superconformal algebras. We prove several general results on the ordering kernels associated to the adapted orderings and show that the size of an ordering kernel implies an upper limit for the dimension of a singular vector space. We apply this method to the topological N= 2 algebra and obtain the maximal dimensions of the singular vector spaces in the topological Verma modules: 0, 1, 2 or 3 depending on the type of Verma module and the type of singular vector. As a consequence we prove the conjecture of Gato-Rivera and Rosado on the possible existing types of topological singular vectors (4 in chiral Verma modules and 29 in complete Verma modules). Interestingly, we have found two-dimensional spaces of singular vectors at level 1. Finally, by using the topological twists and the spectral flows, we also obtain the maximal dimensions of the singular vector spaces for the Neveu–Schwarz N= 2 algebra (0, 1 or 2) and for the Ramond N= 2 algebra (0, 1, 2 or 3). Received: 19 August 1998 / Accepted: 15 March 1999     

The Most Effective Model for Describing the Universal Behavior of a Noisy Kuramoto–Sivashinsky Equation as a Paradigmatic Model

We study a noisy Kuramoto–Sivashinsky (KS) equation which describes unstable surface growth and chemical turbulence. It has been conjectured that the universal long-wavelength behavior of the equation, which is characterized by scale-dependent parameters, is described by a Kardar–Parisi–Zhang (KPZ) equation. We consider this conjecture by analyzing a renormalization-group equation for a class of generalized KPZ equations. We then uniquely determine the parameter values of the KPZ equation that most effectively describes the universal long-wavelength behavior of the noisy KS equation.     

Exact Solution of the Milburn Equation for the Two—Mode Two—Photon Jaynes—Cummings Model

We adopt an algebraic method to study the two-mode two-photon Jaynes-Cummings model governed by the Milburn equation and find an exact solution of Milburn equation of the system.The influence of the intrinsic decoherence on the nonclassical effects of the system is also discussed.     

Numerical Determination of the Critical Value for the （1＋1）-Dimensional Sine-Gordon Model

A new procedure of potential importance sampling method is applied to investigate the phase transition of the （1＋1）-dimensional sine-Gordon model. With this method, we obtain the Kosterlitz-Thouless-type phase transition critical value of β^2 ≌ 8π with a relative error as small as 0.4%.     

Multiscale Formalism for Correlation Functions of Fermions. Infrared Analysis of the Tridimensional Gross–Neveu Model

We present a multiscale formalism for fermionic systems (with a smooth UV cutoff ) establishing a trivial link between the correlation functions and the effective potential flow, and study the k-point truncated functions of the tridimensional Gross–Neveu model. A new efficient method is used to bound these correlation functions and show polynomial tree decay for long distances. We are guided by a block lattice mechanism with a property of orthogonality between terms in different scales, which leads to simple formulas for the correlations.     

Asymptotic Behavior of the Magnetization Near Critical and Tricritical Points via Ginzburg–Landau Polynomials

The purpose of this paper is to prove connections among the asymptotic behavior of the magnetization, the structure of the phase transitions, and a class of polynomials that we call the Ginzburg–Landau polynomials. The model under study is a mean-field version of a lattice spin model due to Blume and Capel. It is defined by a probability distribution that depends on the parameters β and K, which represent, respectively, the inverse temperature and the interaction strength. Our main focus is on the asymptotic behavior of the magnetization m(β _n ,K _n ) for appropriate sequences (β _n ,K _n ) that converge to a second-order point or to the tricritical point of the model and that lie inside various subsets of the phase-coexistence region. The main result states that as (β _n ,K _n ) converges to one of these points (β,K), . In this formula γ is a positive constant, and is the unique positive, global minimum point of a certain polynomial g. We call g the Ginzburg–Landau polynomial because of its close connection with the Ginzburg–Landau phenomenology of critical phenomena. For each sequence the structure of the set of global minimum points of the associated Ginzburg–Landau polynomial mirrors the structure of the set of global minimum points of the free-energy functional in the region through which (β _n ,K _n ) passes and thus reflects the phase-transition structure of the model in that region. This paper makes rigorous the predictions of the Ginzburg–Landau phenomenology of critical phenomena and the tricritical scaling theory for the mean-field Blume–Capel model.     

Mixing Time of Markov Chains for the 1–2 Model

Journal of Statistical Physics - A 1–2 model configuration is a subset of edges of a hexagonal lattice satisfying the constraint that each vertex is incident to 1 or 2 edges. We introduce...     

On the Critical Behavior, the Connection Problem and the Elliptic Representation of a Painlevé VI Equation

In this paper we find a class of solutions of the sixth Painlevé equation appearing in the theory of WDVV equations. This class covers almost all the monodromy data associated to the equation, except one point in the space of the data. We describe the critical behavior close to the critical points in terms of two parameters and we find the relation among the parameters at the different critical points (connection problem). We also study the critical behavior of Painlevé transcendents in the elliptic representation.     

An Iterative Construction of Solutions of the TAP Equations for the Sherrington–Kirkpatrick Model

We propose an iterative scheme for the solutions of the TAP-equations in the Sherrington–Kirkpatrick model which is shown to converge up to and including the de Almeida–Thouless line. The main tool is a representation of the iterations which reveals an interesting structure of them. This representation does not depend on the temperature parameter, but for temperatures below the de Almeida–Thouless line, it contains a part which does not converge to zero in the limit.     

On the Coupling Time of the Heat-Bath Process for the Fortuin–Kasteleyn Random–Cluster Model

We consider the coupling from the past implementation of the random–cluster heat-bath process, and study its random running time, or coupling time. We focus on hypercubic lattices embedded on tori, in dimensions one to three, with cluster fugacity at least one. We make a number of conjectures regarding the asymptotic behaviour of the coupling time, motivated by rigorous results in one dimension and Monte Carlo simulations in dimensions two and three. Amongst our findings, we observe that, for generic parameter values, the distribution of the appropriately standardized coupling time converges to a Gumbel distribution, and that the standard deviation of the coupling time is asymptotic to an explicit universal constant multiple of the relaxation time. Perhaps surprisingly, we observe these results to hold both off criticality, where the coupling time closely mimics the coupon collector’s problem, and also at the critical point, provided the cluster fugacity is below the value at which the transition becomes discontinuous. Finally, we consider analogous questions for the single-spin Ising heat-bath process.     

Critical Pressure of the Structure I Empty Gas Hydrate

A 368 water molecule structure I empty gas hydrate with possible minimum energy are calculated under high pressures by using TIP4P potential molecular dynamical simulations.Thermodynamical properties are analysed.Radial Distribution function and phonon density of states shows that there is a phase transition to high-density ice at low temperature.     

Effect of Quantum Jumpers on the Critical Supercurrent in Dirty S–I–S Junctions

It has been shown that the presence of narrowband quantum jumpers in “dirty” (low concentrations of identical nonmagnetic impurities in the insulator (I) layer) S–I–S (S is a superconductor) junctions at the temperature T = 0 significantly reduces the critical supercurrent (Josephson current) as compared to the value given by the known the Ambegaokar–Baratoff relation. The performed estimates have shown the possibility of the experimental manifestation of this effect.