Conformal Invariance and SLE in Two-Dimensional Ising Spin Glasses

Details Conformal Invariance and SLE in Two-Dimensional Ising Spin Glasses Conformal Invariance and SLE in Two-Dimensional Ising Spin Glasses

2006-01-31

arxiv.org/abs/cond-mat/0601711v3

Phys. Rev. Lett. 97, 267202 (2006).

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 4 figures, changed title and discussion, additional discussion of Markov property; discussion of Markov property remo

Scientific paper

10.1103/PhysRevLett.97.267202

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 $\kappa \approx 2.1$. An argument is given that their fractal dimension $d_f$ is related to their interface energy exponent $\theta$ by $d_f-1=3/[4(3+\theta)]$, which is consistent with the commonly quoted values $d_f \approx 1.27$ and $\theta \approx -0.28$.

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