Possible description of domain walls in two-dimensional spin glasses by stochastic Loewner evolutions

Abstract

Domain walls for spin glasses are believed to be scale 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 ${\mathrm{SLE}}_{\ensuremath{\kappa}}$. Multiple tests are consistent with ${\mathrm{SLE}}_{\ensuremath{\kappa}}$, where $\ensuremath{\kappa}=2.32\ifmmode\pm\else\textpm\fi{}0.08$. 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.