Abstract
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 predictions for the freezing temperature T f and for the zero-field thermodynamic properties and correlation length above T f as a function of dimensionality.
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Kierlik, E., Rosinberg, M.L. & Tarjus, G. A Self-Consistent Ornstein–Zernike Approximation for the Edwards–Anderson Spin-Glass Model. Journal of Statistical Physics 100, 423–443 (2000). https://doi.org/10.1023/A:1018612317044
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DOI: https://doi.org/10.1023/A:1018612317044