Correlation asymptotics for non-translation invariant lattice spin systems
نویسنده
چکیده
We obtain asymptotic expressions for the Green kernels of certain non-translation invariant transition matrices using methods of semiclassical and microlocal analysis. Combined with a result by Bach and Møller this yields asymptotic formulas for the truncated two-point correlation functions of certain non-translation invariant lattice models of real-valued spins.
منابع مشابه
Detailed balance and split property in quantum spin chain
In this exposition we investigate further the general methodology proposed in [Mo2] to study properties of the ground states of a translation invariant Hamiltonian for one lattice dimensional quantum spin chain A = ⊗ZZMd, where Md is the matrix of d × d complex matrices. We introduce a notion of quantum detailed balance [Mo1] for a translation invariant state on A and prove that such a pure sta...
متن کاملPhase transition and split property in quantum spin chain
In this exposition we investigate further the methodology developed in [Mo2] to study properties of the ground states of a translation invariant Hamiltonian for one lattice dimensional quantum spin chain A = ⊗ZZMd, where Md is the space of d × d complex matrices. To that end we study the associated Cuntz elements [Mo2] representing a translation invariant pure state and find an useful criteria ...
متن کاملSU(2) symmetry breaking in quantum spin chain
Though our primary motivation is to study properties of the ground states of a Hamiltonian for quantum spin chain, in this exposition we propose a general methodology valid for a translation invariant state. To that end we study the associated Popescu systems [Po,BJKW] representing the translation invariant state and find an useful criteria for the state to be pure. As a simple consequence of t...
متن کاملCorrelation Asymptotics of Classical Lattice Spin Systems with Nonconvex Hamilton Function at Low Temperature. Bjs-1, August 4, 98
The present paper continues Sjj ostrand's study 13] of correlation functions of lattice eld theories by means of Witten's deformed Lapla-cian. Under the assumptions speciied in the paper and for suuciently low temperature, we derive an estimate for the spectral gap of a certain Witten Laplacian which enables us to prove the exponential decay of the two-point correlation function and, further, t...
متن کاملNon-Translation Invariant Gibbs States with Coexisting Phases I. Existence of Sharp Interface for Widom-Rowlinson Type Lattice Models in Three Dimensions*
We investigate the spatially inhomogeneous states of two component, A — B, Widom-Rowlinson type lattice systems. When the fugacity of the two components are equal and large, these systems can exist in two different homogeneous (translation invariant) pure phases one ^4-rich and one B-ήch. We consider now the system in a box with boundaries favoring the segregation of these two phases into "top ...
متن کامل