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

Denis Bernard·Pierre Le Doussal·A. Alan Middleton
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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$_κ$. Multiple tests are consistent with SLE$_κ$, where $κ=2.30(5)$. 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.

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Denis Bernard, Pierre Le Doussal, A. Alan Middleton. 2006-11-16. Are Domain Walls in Spin Glasses Described by Stochastic Loewner Evolutions?. https://doi.org/10.1103/physrevb.76.020403

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