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

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

1996-03-30

arxiv.org/abs/cond-mat/9603195v1

Physics

Condensed Matter

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

Scientific paper

10.1103/PhysRevB.54.364

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 $\gamma=1.805\pm0.02$ 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 $\gamma=1.435\pm 0.015$, $\nu=0.678\pm 0.05$.

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