Abstract
The ground state entropy of the 2D Ising spin glass with +1 and −1 bonds is studied for L×M square lattices with L≤M and p=0.5, where p is the fraction of negative bonds, using periodic and/or antiperiodic boundary conditions. From this we obtain the domain wall entropy as a function of L and M. It is found that for domain walls which run in the short, L direction, there are finite-size scaling functions which depend on the ratio \(M/L^{d_{S}}\) , where d S =1.22±0.01. When M is larger than L, very different scaling forms are found for odd L and even L. For the zero-energy domain walls, which occur when L is even, the probability distribution of domain wall entropy becomes highly singular, and apparently multifractal, as \(M/L^{d_{S}}\) becomes large.
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Fisch, R. Aspect-Ratio Scaling of Domain Wall Entropy for the 2D ±J Ising Spin Glass. J Stat Phys 130, 561–569 (2008). https://doi.org/10.1007/s10955-007-9436-4
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DOI: https://doi.org/10.1007/s10955-007-9436-4