Proof of entropic order in Generalized Ising Models

TL;DR

This paper rigorously proves the existence of entropic order at high temperatures in generalized Ising models and links these models to solving graph packing problems, revealing potential glassy phases.

Contribution

It provides a rigorous proof of entropic order in generalized Ising models and connects these models to solving NP-hard graph packing problems.

Findings

Proof of entropic order in generalized Ising models for p ≥ 1.

Models solve graph packing problems, including Maximum Independent Set.

Identification of entropic glass phases due to NP-hardness.

Abstract

Ordering at arbitrarily high temperature - entropic order - has been argued to take place in a class of generalized Ising models parameterised by a real interaction parameter $p$ when $p\ge 1$. We give a rigorous proof of this conjecture. We further show that on arbitrary graphs, these models solve graph packing problems - crucially, the Maximum Independent Set optimisation problem. Due to the NP-hardness of this packing problem on generic graphs, some lattice systems will exhibit glassy phases. We call this phenomenon $entropic$ $glass$.