High Temperature Expansion Study of the Nishimori multicritical Point in Two and Four Dimensions

Abstract

We study the two and four dimensional Nishimori multicritical point via high temperature expansions for the $\pm J$ distribution, random-bond, Ising model. In $2d$ we estimate the the critical exponents along the Nishimori line to be $\gamma =2.37\pm 0.05$, $\nu =1.32\pm 0.08$. These, and earlier $3d$ estimates $\gamma =1.80\pm 0.15$, $\nu =0.85\pm 0.08$ are remarkably close to the critical exponents for percolation, which are known to be $\gamma =43/18$, $\nu =4/3$ in $d=2$ and $\gamma =1.805\pm 0.02$ and $\nu =0.875\pm 0.008$ in $d=3$. However, the estimated $4d$ Nishimori exponents $\gamma =1.80\pm 0.15$, $\nu =1.0\pm 0.1$, are quite distinct from the $4d$ percolation results $\gamma =1.435\pm 0.015$, $\nu =0.678\pm 0.05$.

5 pages, RevTex, 3 postscript files; To appear in Physical Review B

References in corpus (2)

• Scaling Theory of the Integer Quantum Hall Effect
• High-Temperature Series Analyses of the Classical Heisenberg and XY Model

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