The Kac limit for finite-range spin glasses

Abstract

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 $\gamma \to 0$. This could be a first step toward an expansion around mean field theory, for spin glass systems.

4 pages; references updated, typos corrected

References in corpus (3)

• Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
• The Thermodynamic Limit in Mean Field Spin Glass Models
• Ordering and Broken Symmetry in Short-Ranged Spin Glasses

Cited by in corpus (18)

• Spontaneous and induced dynamic correlations in glass-formers II: Model calculations and comparison to numerical simulations
• Analytic determination of dynamical and mosaic length scales in a Kac glass model
• Dynamical transition of glasses: from exact to approximate
• Glassy behavior of light in random lasers
• First steps of a nucleation theory in disordered systems
• Metastable States, Relaxation Times and Free-energy Barriers in Finite Dimensional Glassy Systems
• Finite-range spin glasses in the Kac limit: free energy and local observables
• Glassy dynamics as a melting process (On melting dynamics and the glass transition, Part II)
• Dynamical Landau Theory of the Glass Crossover
• Solvable Models of Supercooled Liquids in Three Dimensions
• A field-theoretical approach to the spin glass transition: models with long but finite interaction range
• On the dynamics of Kac $p$-spin glasses
• Surface Tension in Kac Glass Models
• Local Spin Glass Order in 1D
• Mosaic length and finite interaction-range effects in a one dimensional random energy model
• Mean-field theory is exact for Ising spin glass models with Kac potential in non-additive limit on Nishimori line
• Spin glass models with Kac interactions
• A simple one dimensional glassy Kac model