Minimal Models of Entropic Order

TL;DR

This paper introduces minimal classical and quantum models demonstrating that entropic effects can induce order and spontaneous symmetry breaking at high temperatures, challenging traditional notions of disorder in thermodynamics.

Contribution

It presents the Arithmetic Ising Model and its quantum analogue as simple models showing entropic order and high-temperature symmetry breaking.

Findings

High-temperature phases are ordered in classical and quantum models.

Entropic effects can lead to spontaneous symmetry breaking at high temperatures.

Classical gas models can form crystals driven by interactions at high temperatures.

Abstract

Due to entropic effects, it is possible that generic high-energy states of a quantum or classical system are ordered. This leads to spontaneous symmetry breaking at arbitrarily high temperatures. We present minimal models of entropic order that arise from very simple interactions. Our main examples are the Arithmetic Ising Model (AIM) and its quantum analogue, where usual Ising spins are replaced by non-negative integers. Using a large-flavor expansion together with numerical simulations, we find that the high-temperature phase is ordered in the classical and quantum models. We also introduce classical gas models whose interactions drive the system to a crystal at high temperatures.