Temperature-Resistant Order in 2+1 Dimensions

TL;DR

This paper demonstrates that in certain 2+1 dimensional quantum field theories, order can persist at high temperatures, challenging the common notion that increased temperature always leads to disorder.

Contribution

The authors introduce a new class of local, unitary models in 2+1 dimensions where symmetry breaking occurs at all temperatures, including high temperatures.

Findings

Symmetry breaking $ ext{Z}_2 o ext{empty}$ occurs at any temperature in some models.

Identified UV-complete, local, unitary models with this property.

Phenomenon previously observed only in fractional dimensions or non-local models.

Abstract

High temperatures are typically thought to increase disorder. Here we examine this idea in Quantum Field Theory in 2+1 dimensions. For this sake we explore a novel class of tractable models, consisting of nearly-mean-field scalars interacting with critical scalars. We identify UV-complete, local, unitary models in this class and show that symmetry breaking $\mathbb{Z}_2 \to \emptyset$ occurs at any temperature in some regions of the phase diagram. This phenomenon, previously observed in models with fractional dimensions, or in the strict planar limits, or with non-local interactions, is now exhibited in a local, unitary 2+1 dimensional model with a finite number of fields.