Spin glass models with Kac interactions
نویسنده
چکیده
In this paper I will review my work on disordered systems -spin glass model with two body and p > 2 body interactionswith long but finite interaction range R. I will describe the relation of these model with Mean Field Theory in the Kac limit and some attempts to go beyond mean field. PACS. 0 5.20.-y,75.10Nr
منابع مشابه
Some comments on the connection between disordered long range spin glass models and their mean field version
In this paper, we consider a particular aspect of the relationship between mean field and finite-dimensional spin glasses. By means of a simple interpolation method, we prove that the free energy of a class of finite dimensional spin glass models with Kac-type interactions is bounded below by that of their mean field analog. As a result, Parisi theory of replica symmetry breaking can be exploit...
متن کاملKac limit for finite-range spin glasses.
We consider a finite-range spin glass model in arbitrary dimension, where the strength of the two-body coupling decays to zero over some distance gamma(-1). We show that, under mild assumptions on the interaction potential, the infinite-volume free energy of the system converges to that of the Sherrington-Kirkpatrick one, in the Kac limit gamma-->0. This could be a first step toward an expansio...
متن کاملFinite-range spin glasses in the Kac limit: free energy and local observables
We study a finite-range spin-glass model in arbitrary dimension, where the intensity of the coupling between spins decays to zero over some distance γ−1. We prove that, under a positivity condition for the interaction potential, the infinite-volume free energy of the system converges to that of the Sherrington– Kirkpatrick model, in the Kac limit γ → 0. We study the implication of this converge...
متن کاملA simple one dimensional glassy Kac model
We define a new family of random spin models with one-dimensional structure, finite-range multi-spin interactions, and bounded average degree (number of interactions in which each spin participates). Unfrustrated ground states can be described as solutions of a sparse, band diagonal linear system, thus allowing for efficient numerical analysis. In the limit of infinite interaction range, we rec...
متن کاملCritical behaviour and ultrametricity of Ising spin-glass with long-range interactions
Ising spin-glass systems with long-range interactions (J(r) ∼ r) are considered. A numerical study of the critical behaviour is presented in the non-mean-field region together with an analysis of the probability distribution of the overlaps and of the ultrametric structure of the space of pure states in the frozen phase. Also in presence of diverging thermodynamical fluctuations at the critical...
متن کامل