Modern Physics Letters B

THE ANNEALED MANY-BONDS ISING MODEL

P. Marko, Martin Kupka, P. Kopčanský

Published Mar 10, 1991• 0 citations

Abstract

The random bond problem with many kinds of bonds for Ising lattice is studied. The transformation was found from the Ising model with many kinds of bonds to the Ising problem with one effective bond. The method of transformation is illustrated on the 2D square lattice with ferromagnetic and antiferromagnetic interactions.

DOI: 10.1142/s021798499100054x

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Modern Physics Letters B

THE ANNEALED MANY-BONDS ISING MODEL

P. Marko, Martin Kupka, P. Kopčanský

Published Mar 10, 1991• 0 citations

Publisher

Abstract

DOI: 10.1142/s021798499100054x

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{M}^{3},

and not exponential in M as with conventional algorithms. We show how the approach may be used to calculate for the RBIM the free energy, typical correlation lengths in quasi-one dimension for both the spin and the disorder operators, and the even powers of spin-spin correlation functions and their disorder averages. We examine in detail the square-lattice, nearest-neighbor $\ifmmode\pm\else\textpm\fi{}J$ RBIM, in which bonds are independently antiferromagnetic with probability p, and ferromagnetic with probability $1\ensuremath{-}p.$ Studying temperatures

T>~0.4J,

we obtain precise coordinates in the $p\ensuremath{-}T$ plane for points on the phase boundary between ferromagnet and paramagnet, and for the multicritical (Nishimori) point. We demonstrate scaling flow towards the pure Ising fixed point at small p, and determine critical exponents at the multicritical point.