Constrained annealing for spin glasses

TL;DR

This paper introduces a new method for estimating the free energy of spin glasses by constraining frustration in annealed averages, providing converging lower bounds for 2D models without using Lagrange multipliers.

Contribution

A novel approach to compute constrained annealed averages in spin glasses that avoids Lagrange multipliers and yields converging bounds for 2D systems.

Findings

Provides a sequence of lower bounds for 2D spin glass free energy.

Introduces a method using small volume averages and transfer matrices.

Offers a new analytical technique for quenched averages.

Abstract

The quenched free energy of spin glasses is estimated by means of annealed averages where the frustration is constrained to its average value. We discuss the case of d-dimensional Ising models with random nearest neighbour coupling, and we introduce a new method to obtain constrained annealed averages without recurring to Lagrange multipliers. It requires to perform quenched averages either on small volumes in an analytic way, or on finite size strips via products of random transfer matrices. We thus give a sequence of converging lower bounds for the quenched free energy of 2d spin glasses.