# Self-correction in Wegner's 3D Ising lattice gauge theory

## TL;DR

This paper demonstrates that Wegner's 3D Ising lattice gauge model can function as a self-correcting classical memory, extending the understanding of phase stability in systems with gauge symmetries beyond topological phases.

## Contribution

It shows that a classical 3D lattice gauge system can realize self-correction, even with explicit gauge symmetry breaking, expanding the class of systems capable of self-correction.

## Key findings

- Self-correcting phase exists in Wegner's 3D Ising lattice gauge model.
- Self-correction persists beyond the topological phase and lower critical temperature.
- Numerical results align with phase diagram from specific heat analysis.

## Abstract

Motivated by the growing interest in self-correcting quantum memories, we study the feasibility of self-correction in classical lattice systems composed of bounded degrees of freedom with local interactions. We argue that self-correction, including a requirement of stability against external perturbation, cannot be realized in system with broken global symmetries such as the 2d Ising model, but that systems with local, i.e. gauge, symmetries have the required properties. Previous work gave a three-dimensional quantum system which realized a self-correcting classical memory. Here we show that a purely classical three dimensional system, Wegner's 3D Ising lattice gauge model, can also realize this self-correction despite having an extensive ground state degeneracy. We give a detailed numerical study to support the existence of a self-correcting phase in this system, even when the gauge symmetry is explicitly broken. More generally, our results obtained by studying the memory lifetime of the system are in quantitative agreement with the phase diagram obtained from conventional analysis of the system's specific heat, except that self-correction extends beyond the topological phase, past the lower critical temperature.