Equilibrium states for a one dimensional lattice gas

The thermodynamic equilibrium state can be defined directly for an infinite system via an equilibrium condition or via the variational principle. Both definitions are used to calculate the equilibrium state for a one dimensional lattice gas with finite range interactions.     

Equilibrium states for classical systems

It is shown that the Dobrushin-Lanford-Ruelle equations for the probability measure μ, and the Kirkwood-Salsburg type equations for the lattice or continuum correlation functions ?, and for the spin correlation functions σ, are essentially equivalent for all ?, σ, and μ satisfying certain boundedness conditions. It is also noted that the lattice equations are identical to the equations for the stationary states of a certain Markoff process. This extends previous results of Ruelle, Brascamp and Holley who proved some of these equivalences for states.     

Equilibrium states of a semi-quantum lattice system

As an intermediate situation between quantum and classical lattice systems we investigate a semi-quantum lattice system (such as an alloy of several kinds of atoms). The relevant observable algebra is a special type of AF algebras. We study equilibrium states of the system and obtain some equivalent equilibrium conditions.     

Ground states of a classical triangular lattice

The energies and displacements of a triangular lattice with nearest and next-nearest neighbor interaction are calculated for the groundstates. A nonlinear onsite potential acts perpendicular to the plane. Structures with low periodicity determine the various states in the parameter space. The stability of the different phases is investigated.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

Equilibrium and metastable states of classical systems

We formulate a characterization of equilibrium and metastable states of classical hard-core continuous systems in terms of certain global and local stability conditions. The equilibrium states are assumed to be those that are both locally and globally stable; the metastable states are assumed to be those that are locally, but not globally, stable, and that possess also a certain restricted global stability. It is found that a certain specified class of systems with appropriately weakly tempered, or long range forces, can support metastable states, possessing bona fide thermodynamic properties, whose pressure functions are real analytic continuations in the chemical potential of those of some equilibrium phases. This result is complementary to that of Lanford and Ruelle, concerning the absence of metastable states of systems with strongly tempered forces.     

Matrix-product states for a one-dimensional lattice gas with parallel dynamics

The hopping motion of classical particles on a chain coupled to reservoirs at both ends is studied for parallel dynamics with arbitrary probabilities. The stationary state is obtained in the form of an alternating matrix product. The properties of one- and two-dimensional representations are studied in detail and a general relation of the matrix algebra to that of the sequential limit is found. In this way the general phase diagram of the model is obtained. The mechanism of the sequential limit, the formulation as a vertex model, and other aspects are discussed.     

Ground states in classical lattice systems with hard core

In this paper we prove the existence of translation invariant ground states in an infinite classical lattice system with hard core and give a characterization of their support. Some examples are discussed.     

Persistence distributions in a conserved lattice gas with absorbing states

Extensive simulations are performed to study the persistence behavior of a conserved lattice gas model exhibiting an absorbing phase transition from an active phase into an inactive phase. Both the global and the local persistence exponents are determined in two and higher dimensions. The local persistence exponent obeys a scaling relation involving the order parameter exponent of the absorbing phase transition. Furthermore we observe that the global persistence exponent exceeds its local counterpart in all dimensions in contrast to the known persistence behavior in reversible phase transitions. Received 27 August 2001 and Received in final form 15 November 2001     

Hydrodynamics of stationary non-equilibrium states for some stochastic lattice gas models

We consider discrete lattice gas models in a finite interval with stochastic jump dynamics in the interior, which conserve the particle number, and with stochastic dynamics at the boundaries chosen to model infinite particle reservoirs at fixed chemical potentials. The unique stationary measures of these processes support a steady particle current from the reservoir of higher chemical potential into the lower and are non-reversible. We study the structure of the stationary measure in the hydrodynamic limit, as the microscopic lattice size goes to infinity. In particular, we prove as a law of large numbers that the empirical density field converges to a deterministic limit which is the solution of the stationary transport equation and the empirical current converges to the deterministic limit given by Fick's law.Dedicated to Res Jost and Arthur WightmanSupported in part by NSF Grants DMR 89-18903 and INT 8521407. H.S. also supported by the Deutsche Forschungsgemeinschaft     

Energy-entropy inequalities for classical lattice systems

A new characterization of equilibrium states for classical lattice systems is given in terms of correlation inequalities. Their physical meaning is found to express thermodynamic stability. We demonstrate the applicability of the inequalities in specific models.Bevoegdverklaard navorser N.F.W.O.Aangesteld navorser N.F.W.O.     

Metastable states of a gas of dipolar bosons in a 2D optical lattice

We investigate the physics of dipolar bosons in a two-dimensional optical lattice. It is known that due to the long-range character of dipole-dipole interaction, the ground state phase diagram of a gas of dipolar bosons in an optical lattice presents novel quantum phases, like checkerboard and supersolid phases. In this Letter, we consider the properties of the system beyond its ground state, finding that it is characterized by a multitude of almost degenerate metastable states, often competing with the ground state. This makes dipolar bosons in a lattice similar to a disordered system and opens possibilities of using them as quantum memories.     

Field-induced vacancy localization in a driven lattice gas: scaling of steady states

With the help of Monte Carlo simulations and a mean-field theory, we investigate the ordered steady-state structures resulting from the motion of a single vacancy on a periodic lattice which is filled with two species of oppositely "charged" particles. An external field biases particle-vacancy exchanges according to the particle's charge, subject to an excluded volume constraint. The steady state exhibits charge segregation, and the vacancy is localized at one of the two characteristic interfaces. Charge and hole density profiles, an appropriate order parameter, and the interfacial regions themselves exhibit characteristic scaling properties with system size and field strength. The lattice spacing is found to play a significant role within the mean-field theory.     

Analyticity and uniqueness of the invariant equilibrium states for general spin 1/2 classical lattice systems

Asano-Ruelle-Slawny method is generalized to discuss analyticity and uniqueness of the correlation functions in terms of the group structure associated with any lattice systems. The use of Poisson formula for abelian groups gives a simple method to obtain explicit domains where the above properties are verified.     

Dynamics of a lattice gas

A stochastic model whose ergodic variant coincides with the Ising model has been considered. Constraints following from a microscopic conservation law are imposed on dynamics (lattice gas model). The master equation for the dynamic correlation function has been derived. It has been shown that the separation curve on the density-temperature diagram for the initial microdispersed state lies below that predicted by the Gibbs statistics. Furthermore, not only the position but also the shape of the entire curve can change: it becomes double humped rather than dome shaped.     

Passive states for finite classical systems

Starting from a passivity condition based on the second law of thermodynamics [12], we show that ground states and Gibbs states (0<<) are essentially the only passive states.Research supported by M. Skodowska-Curie Fund Grant No. OIP74-01416.     

Crystalline ground states for classical particles

Pair interactions whose Fourier transform is non-negative and vanishes above a wave number K(0) are shown to give rise to periodic and aperiodic infinite volume ground state configurations (GSCs) in any dimension d. A typical three-dimensional example is an interaction of asymptotic form cosK(0)r/r(4). The result is obtained for densities rho > or = rho(d), where rho(1) = K(0)/2(pi), rho(2) = (sq.rt(3)/8)(K(0)/pi)(2), and rho(3) = (1/8sq.rt(2)) x (K(0)/pi)(3). At rho(d) there is a unique periodic GSC which is the uniform chain, the triangular lattice, and the bcc lattice for d = 1,2,3, respectively. For rho > rho(d), the GSC is nonunique and the degeneracy is continuous: Any periodic configuration of density rho with all reciprocal lattice vectors not smaller than K(0), and any union of such configurations, is a GSC. The fcc lattice is a GSC only for rho > or = (1/6 sq.rt(3)) x (K(0)/pi)(3).