The Stability of the Replica Symmetric State in Finite Dimensional Spin Glasses

Abstract

According to the droplet picture of spin glasses, the low-temperature phase of spin glasses should be replica symmetric. However, analysis of the stability of this state suggested that it was unstable and this instability lends support to the Parisi replica symmetry breaking picture of spin glasses. The finite-size scaling functions in the critical region of spin glasses below T_c in dimensions greater than 6 can be determined and for them the replica symmetric solution is unstable order by order in perturbation theory. Nevertheless the exact solution can be shown to be replica-symmetric. It is suggested that a similar mechanism might apply in the low-temperature phase of spin glasses in less than six dimensions, but that a replica symmetry broken state might exist in more than six dimensions.

5 pages. Modified to include a paragraph on the relation of this work to that of Newman and Stein

References in corpus (4)

• Absence of an Almeida-Thouless line in Three-Dimensional Spin Glasses
• Ordering and Broken Symmetry in Short-Ranged Spin Glasses
• A Study of Inclusive Double-Pomeron-Exchange in p pbar -> p X pbar at root s = 630 GeV
• Nature of perturbation theory in spin glasses

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• The 1/m expansion in spin glasses and the de Almeida-Thouless line
• Low-temperature spin-glass behaviour in a diluted dipolar Ising system
• Replica symmetric spin glass field theory
• Numerical results for the Edwards-Anderson spin-glass model at low temperature
• Pair correlation function for spin glasses
• Correlated Domains in Spin Glasses