UV complete local field theory of persistent symmetry breaking in 2+1 dimensions

TL;DR

This paper demonstrates a UV complete local field theory in 2+1 dimensions that exhibits persistent symmetry breaking at all temperatures, using functional methods to analyze quantum critical behavior and phase transitions.

Contribution

It provides the first direct 2+1 dimensional local model showing persistent symmetry breaking, with detailed phase diagram and critical N, respecting the Mermin-Wagner theorem.

Findings

Quantum critical behavior accurately described for all N≥2.

Discrete symmetry breaking occurs near the biconical critical point for large N.

Critical N for symmetry breaking is approximately 15.

Abstract

Spontaneous symmetry breaking can persist at all temperatures in certain biconical $\mathrm{O}(N)\times \mathbb{Z}_2$ vector models when the underlying field theories are ultraviolet complete. So far, the existence of such theories has been established in fractional dimensions for local but nonunitary models or in 2+1 dimensions but for nonlocal models. Here, we study local models at zero and finite temperature directly in 2+1 dimensions employing functional methods. At zero temperature, we establish that our approach describes the quantum critical behaviour with high accuracy for all $N\geq 2$. We then exhibit the mechanism of discrete symmetry breaking from $\mathrm{O}(N)\times \mathbb{Z}_2\to \mathrm{O}(N)$ for increasing temperature near the biconical critical point when $N$ is finite but large. We calculate the corresponding finite-temperature phase diagram and further show that the Hohenberg-Mermin-Wagner theorem is fully respected within this approach, i.e., symmetry breaking only occurs in the $\mathbb{Z}_2$ sector. Finally, we determine the critical $N$ above which this phenomenon can be observed to be $N_c \approx 15$.