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A variational approach to Ising spin glasses in finite dimensions

R. Baviera·M. Pasquini·M. Serva
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Abstract

We introduce a hierarchical class of approximations of the random Ising spin glass in $d$ dimensions. The attention is focused on finite clusters of spins where the action of the rest of the system is properly taken into account. At the lower level (cluster of a single spin) our approximation coincides with the SK model while at the highest level it coincides with the true $d$-dimensional system. The method is variational and it uses the replica approach to spin glasses and the Parisi ansatz for the order parameter. As a result we have rigorous bounds for the quenched free energy which become more and more precise when larger and larger clusters are considered.

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R. Baviera, M. Pasquini, M. Serva. 1997-11-04. A variational approach to Ising spin glasses in finite dimensions. https://doi.org/10.1088/0305-4470%2F31%2F18%2F005

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