Abstract
The replica extension theory has been developed for the purpose of investigating spin glasssystems in the replica symmetry breaking phase. The replica extension theory is a replicatheory for a specific sample and has the scheme of the one-step replica symmetry breakingansatz. In this paper, using the Plefka expansion, we propose the perturbative expansion ofGibbs free energies of Ising systems with the replica extension theory, and we derive theexplicit form of the second- and third-order approximations. Our Plefka expansionsystematically provides perturbative approximations taking the one-step replica symmetrybreaking into account. In some numerical experiments, we show that our perturbativeapproximations are quantitatively superior to conventional perturbative approximationsthat do not take the one-step replica symmetry breaking into account in the spin glassphase.
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