Spin glass field theory with replica Fourier transforms
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Publication:2936387
DOI10.1088/1751-8113/47/45/455001zbMATH Open1312.82023arXiv1412.8688OpenAlexW3105528443MaRDI QIDQ2936387
Author name not available (Why is that?)
Publication date: 16 December 2014
Published in: (Search for Journal in Brave)
Abstract: We develop a field theory for spin glasses using Replica Fourier Transforms (RFT). We present the formalism for the case of replica symmetry and the case of replica symmetry breaking on an ultrametric tree, with the number of replicas and the number of replica symmetry breaking steps generic integers. We show how the RFT applied to the two-replica fields allows to construct a new basis which block-diagonalizes the four-replica mass-matrix, into the replicon, anomalous and longitudinal modes. The eigenvalues are given in terms of the mass RFT and the propagators in the RFT space are obtained by inversion of the block-diagonal matrix. The formalism allows to express any -replica vertex in the new RFT basis and hence enables to perform a standard perturbation expansion. We apply the formalism to calculate the contribution of the Gaussian fluctuations around the Parisi solution for the free-energy of an Ising spin glass.
Full work available at URL: https://arxiv.org/abs/1412.8688
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