Gaussian Mean Fields Lattice Gas

TL;DR

This paper rigorously analyzes a lattice gas version of the SK spin glass model, proving ground state energy fluctuations vanish in large systems, and introduces a probabilistic cellular automaton heuristic for near-optimal solutions.

Contribution

It provides a rigorous analysis of the lattice gas SK model and proposes a novel heuristic algorithm for large instances.

Findings

Ground state energy fluctuations tend to vanish in the thermodynamic limit.

A lower bound for the ground state energy is established.

The heuristic algorithm effectively finds near-minimum energy configurations.

Abstract

We study rigorously a lattice gas version of the Sherrington-Kirckpatrick spin glass model. In discrete optimization literature this problem is known as Unconstrained Binary Quadratic Programming (UBQP) and it belongs to the class NP-hard. We prove that the fluctuations of the ground state energy tend to vanish in the thermodynamic limit, and we give a lower bound of such ground state energy. Then we present an heuristic algorithm, based on a probabilistic cellular automaton, which seems to be able to find configurations with energy very close to the minimum, even for quite large instances.