A self-consistent Ornstein-Zernike approximation for the Edwards-Anderson spin glass model

Details A self-consistent Ornstein-Zernike approximation for the Edwards-Anderson spin glass model A self-consistent Ornstein-Zernike approximation for the Edwards-Anderson spin glass model

1999-09-13

arxiv.org/abs/cond-mat/9909180v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

19 pages, 1 figure. submitted to J. Stat. Phys

Scientific paper

We propose a self-consistent Ornstein-Zernike approximation for studying the Edwards-Anderson spin glass model. By performing two Legendre transforms in replica space, we introduce a Gibbs free energy depending on both the magnetizations and the overlap order parameters. The correlation functions and the thermodynamics are then obtained from the solution of a set of coupled partial differential equations. The approximation becomes exact in the limit of infinite dimension and it provides a potential route for studying the stability of the high-temperature phase against replica-symmetry breaking fluctuations in finite dimensions. As a first step, we present the numerical predictions for the freezing temperature and the zero-field thermodynamic properties above freezing as a function of dimensionality.

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