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Conformal Invariance and SLE in Two-Dimensional Ising Spin Glasses

C. Amoruso·A. K. Hartmann·M. B. Hastings·M. A. Moore
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Abstract

We present numerical evidence that the techniques of conformal field theory might be applicable to two-dimensional Ising spin glasses with Gaussian bond distributions. It is shown that certain domain wall distributions in one geometry can be related to that in a second geometry by a conformal transformation. We also present direct evidence that the domain walls are stochastic Loewner (SLE) processes with $κ\approx 2.1$. An argument is given that their fractal dimension $d_f$ is related to their interface energy exponent $θ$ by $d_f-1=3/[4(3+θ)]$, which is consistent with the commonly quoted values $d_f \approx 1.27$ and $θ\approx -0.28$.

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C. Amoruso, A. K. Hartmann, M. B. Hastings, M. A. Moore. 2006-10-28. Conformal Invariance and SLE in Two-Dimensional Ising Spin Glasses. https://doi.org/10.1103/physrevlett.97.267202

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