A variational approach to Ising spin glasses in finite dimensions
arXiv:cond-mat/9711026 · doi:10.1088/0305-4470/31/18/005
Abstract
We introduce a hierarchical class of approximations of the random Ising spin glass in 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 -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.
16 pages, Plain TeX, uses Harvmac.tex, 4 ps figures, submitted to J. Phys. A: Math. Gen