Abstract
Using real replicas to describe the many-state phase space of the Sherrington-Kirkpatrick model of a spin glass, we rederive the Sompolinsky free energy for the ground state. We propose an interpretation of the order parameter function q(x), x ε 〈0,1〉, from the Sompolinsky free energy directly within the real replica scheme. We also suggest an iterative way of reaching the ground-state (Sompolinsky) free energy within this scheme and present numerical results for the first iteration going beyond the ergodic (replica symmetric) solution.
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The authors are grateful to the referee for constructive comments leading to improvements in the construction of the Sompolinsky free energy and the following interpretation.
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Janiš, V., Mašek, J. New interpretation of Parisi-Sompolinsky mean-field solution for spin glasses. Czech J Phys 41, 359–372 (1991). https://doi.org/10.1007/BF01599036
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DOI: https://doi.org/10.1007/BF01599036