Nature of perturbation theory in spin glasses
Abstract
The high-order behavior of the perturbation expansion in the cubic replica field theory of spin glasses in the paramagnetic phase has been investigated. The study starts with the zero-dimensional version of the replica field theory and this is shown to be equivalent to the problem of finding finite size corrections in a modified spherical spin glass near the critical temperature. We find that the high-order behavior of the perturbation series is described, to leading order, by coefficients of alternating signs (suggesting that the cubic field theory is well-defined) but that there are also subdominant terms with a complicated dependence of their sign on the order. Our results are then extended to the d-dimensional field theory and in particular used to determine the high-order behavior of the terms in the expansion of the critical exponents in a power series in epsilon=6-d. We have also corrected errors in the existing epsilon expansions at third order.
Keywords
Cite
@article{arxiv.cond-mat/0501428,
title = {Nature of perturbation theory in spin glasses},
author = {J. Yeo and M. A. Moore and T. Aspelmeier},
journal= {arXiv preprint arXiv:cond-mat/0501428},
year = {2009}
}
Comments
12 pages, 7 figures