Are Domain Walls in Spin Glasses Described by Stochastic Loewner Evolutions?

TL;DR

This paper investigates whether two-dimensional spin glass domain walls can be described by Schramm-Loewner evolution (SLE), providing numerical evidence supporting the SLE description and conformal invariance in the continuum limit.

Contribution

The study tests and supports the hypothesis that spin glass domain walls are described by SLE$_$, demonstrating consistency with conformal invariance and domain Markov property in the continuum limit.

Findings

Domain walls are consistent with SLE$_
c$ with   2.30(5)

Conformal invariance is supported in the continuum limit

Domain Markov property holds in the continuum limit

Abstract

Domain walls for spin glasses are believed to be scale invariant invariant; a stronger symmetry, conformal invariance, has the potential to hold. The statistics of zero-temperature Ising spin glass domain walls in two dimensions are used to test the hypothesis that these domain walls are described by a Schramm-Loewner evolution SLE$_\kappa$. Multiple tests are consistent with SLE$_\kappa$, where $\kappa=2.30(5)$. Both conformal invariance and the domain Markov property are tested. The latter does not hold in small systems, but detailed numerical evidence suggests that it holds in the continuum limit.