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Ordering temperatures and critical exponents in Ising spin glasses

By L. W. Bernardi, S. Prakash, I. A. Campbell and Université Paris Sud

Abstract

We propose a numerical criterion which can be used to obtain accurate and reliable values of the ordering temperatures and critical exponents of spin glasses. Using this method we find a value of the ordering temperature for the ±J Ising spin glass in three dimensions which is definitely non-zero and in good agreement with previous estimates. We show that the critical exponents of three dimensional Ising spin glasses do not appear to obey the usual universality rules. The full explanation of the universality rules for critical exponents in second order transitions through the renormalization group theory is one of the most impressive achievements of statistical physics. The universality rules for such transitions state that the critical exponents depend only on the space dimension d and a few basic parameters: the number of order parameter components n, the symmetry and the range of the Hamiltonian [1]. No other parameters are pertinent. In fact it is known that there are exceptions to universality-in certain two dimensional (2d) Ising systems with regular frustration the critical exponents vary continuously with the value of a control parameter [2]. As far as we are aware, n

Year: 2008
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