Translation invariant equilibrium states of ferromagnetic Abelian lattice systems

The structure of the set of all translation invariant equilibrium states is determined for all temperatures, for which the free energy is differentiable. Models with several phase transitions are discussed rigorously.     

Global invariants and equilibrium states in lattice gases

It is now well known that, in addition to the physical conserved quantities, lattice gases also have other unphysical ones related to the discretization of their phase space. From an abstract point of view a lattice gas can be considered like a full discrete Markov processL and these spurious conserved quantities yield the existence of a nonspatially homogeneous equilibrium state forL ^k. We show that a particular set of these conserved quantities is of special interest: Its elements will be called regular. These regular invariants are simply built from the local ones and their projection on each node is always a locally conserved quantity. Moreover, for most models they are one-to-one related to the Gibbs states ofL ^k which remain factorized. It turns out that all the classical known spurious invariants are regular and one can exhibit simple conditions to build models with only regular invariants. For the latter it is then justified to determine the transport coefficients of the locally conserved densities with the Green-Kubo procedure.     

Biased lattice gases with correlated equilibrium states

The approach to and structure of the equilibrium state is studied for a 7-bit lattice gas with biased forward and backward transition rates by means of mean field theory and computer simulations. If the rate constants obey the factorizability and the detailed balance conditions, the occupations of different velocity directions are uncorrelated, anH-theorem is valid, and a nonuniversal equilibrium state exists that depends explicitly on the transition rates. In case the above conditions are not satisfied, theH-theorem is no longer valid, and mean field theory also predicts nontrivial velocity correlations in postcollision states. The simulations are mainly concentrated on the time dependence of pre- and postcollision velocity correlations on a single node, and on slowly increasing fluctuations that might indicate metastable behavior.     

The property lattice of spatially separated quantum systems

We consider a quantum system composed of two subsystems. Among the properties of this system we study the set of those that can be tested when the subsystems are spatially separated. We show that not all properties satisfy this criterion, but that there are enough such properties to characterize any pure state of the composed system.     

Metastable states of quantum lattice systems

We extend the characterisation of metastability, as given in [1] for classical systems, to show that quantal lattice systems with suitable long range forces can support metastable states.     

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.     

Gibbs states and equilibrium states for finitely presented dynamical systems

We studyfinitely presented dynamical systems (which generalize Axiom A systems) and show that the notions of equilibrium states and Gibbs states (for Hölder continuous functions) are equivalent. Our results extend those of Ruelle, Haydn, and others on Axiom A dynamical systems and statistical mechanics.     

Stability and equilibrium states of infinite classical systems

We prove that any stationary state describing an infinite classical system which is stable under local perturbations (and possesses some strong time clustering properties) must satisfy the classical KMS condition. (This in turn implies, quite generally, that it is a Gibbs state.) Similar results have been proven previously for quantum systems by Haag et al. and for finite classical systems by Lebowitz et al.Supported by N.S.F. Grant MPS 71-03375 A03. Part of this work carried out at the Courant Institute where it was supported by N.S.F. Grant GP-37069X.Supported in part by AFOSR Grant #73-2430 and N.S.F. Grant MP S75-20638.Supported by N.S.F. Grant # GP33136X-2. Part of this work was carried out at the Institute for Advanced Study.     

A characterization of Gibbs states of lattice boson systems

We consider lattice boson systems interacting via potentials which are superstable and regular. By using the Wiener integral formalism and the concept of conditional reduced density matrices we are able to give a characterization of Gibbs (equilibrium) states. It turns out that the space of Gibbs states is nonempty, convex, and also weak-compact if the interactions are of finite range. We give a brief discussion on the uniqueness of Gibbs states and the existence of phase transitions in our formalism.     

Coexistence of antiferromagnetic and ferromagnetic phase for ferromagnetic Kondo lattice model

To study the proposed phase separations in doped manganites, we performed Monte-Carlo calculations for the ferromagnetic Kondo lattice model with strong Hund's coupling between conduction electrons and localized spins. For the practical calculations, we adopted a one dimensional lattice and treated the spins of the localized t_2g electrons semi-classically. A direct evidence of the phase separation is observed from a snapshot of the spatial dependence of localized spins. No indication of the canted or spiral phases is found in the results of simulations. Further, the calculated results of the spin structure factor in the phase separation region are well compared with recent experiments. Received: 1st September 1998 / Revised: 30 October 1998 / Accepted: 27 November 1998     

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.     

Low-temperature expansion for lattice systems with many ground states

Low-temperature expansion for systems with many ground states is discussed. It is pointed out that, in general, different ground states may yield different formal perturbation expansions, and that the right expansion of the free energy is provided by ground states called here dominant.Supported in part by Grant AFOR-78-3522.     

On uniqueness of KMS states of one-dimensional quantum lattice systems

We present a proof of the theorem on the uniqueness of KMS states of one-dimensional quantum lattice systems, which is based on some equicontinuity.     

The unique Jordan-Hahn decomposition property

We show that a finite orthomodular poset with a strong section of states (probability measures) is distributive if and only if has the unique Jordan-Hahn decomposition property(UJHDP). That this result does not extend to infinite orthomodular posets is shown by the projection lattices of von Neumann algebras without direct summand of typeI ₂, for which the set of completely additive states is strong and has theUJHDP. There also exist nondistributive -classes for which the set of countably additive states has theUJHDP.Research supported by Schweizerischer Nationalfonds/Fonds National Suisse under grant number 2.445-0.87.     

Relevance of ferromagnetic correlations for the electron spin resonance in Kondo lattice systems

Electron spin resonance (ESR) measurements of the ferromagnetic (FM) Kondo lattice system CeRuPO show a well defined ESR signal which is related to the Ce3+ magnetism. In contrast, no ESR could be observed in the antiferromagnetic (AFM) homologue CeOsPO. Additionally, we detect an ESR signal in ferromagnetic YbRh while it was absent in a number of Ce or Yb intermetallic compounds with dominant AFM exchange. Thus, the observation of an ESR signal in a Kondo lattice is neither specific to Yb nor to the proximity to a quantum critical point, but seems to be connected to the presence of FM fluctuations. These conclusions not only provide a basic concept to understand the ESR in Kondo lattice systems even well below the Kondo temperature (as observed in YbRh2Si2) but point out ESR as a prime method to investigate directly the spin dynamics of the Kondo ion.     

The global Markov property for equilibrium states which are determined by correlations in a strip

We present a necessary and sufficient condition for the non-existence of rotational invariant circles for area-preserving twist maps of the cyclinder or annulus based on the cone-crossing and killends criteria of MacKay and Percival (1985). Given a number of technical restrictions on the implementation of these criteria, this condition leads to a proof of MacKay and Percival's Finite Computation Conjecture.     

Existence and uniqueness of equilibrium states for some spin and continuum systems

The one to one correspondence between the existence of a unique equilibrium state and the differentiability of the free energy density with respect to the external field previously shown for Ising ferromagnetis is extendend to higher valued spin systems as well as to continuum systems satisfying the Fortuin, Kasteleyn and Ginibre inequalities. In particular this is shown to hold for a mixture ofA –B particles in which there is no interaction between like particles and a repulsion between unlike particles. Where the derivative of the free energy is discontinuous there are at least two equilibrium states.Supported in part by Air Force Grant n. 732430.     

On the equivalence between KMS-states and equilibrium states for classical systems

It is shown that for any KMS-state of a classical system of non-coincident particles, the distribution functions are absolutely continuous with respect to Lebesgue measure; the equivalence between KMS states and Canonical Gibbs States is then established.Supported in part by NSF Grant MCS 75-21684Supported in part by NSF Grant MPS 72-04534Supported in part by NSF Grant MPS 75-20638     

A continuity property of the entropy density for spin lattice systems

The entropy density of spin lattice systems is known to be a weak upper semi-continuous functional on the set of the lattice invariant states. (It is even weak discontinuous.) However we prove here that it is continuous with respect to the norm topology on those states.Aspirant van het Belgisch N.F.W.O.