Summability of the perturbative expansion for a zero-dimensional disordered spin model
Statistical Mechanics
2009-10-31 v1 Disordered Systems and Neural Networks
Abstract
We show analytically that the perturbative expansion for the free energy of the zero dimensional (quenched) disordered Ising model is Borel-summable in a certain range of parameters, provided that the summation is carried out in two steps: first, in the strength of the original coupling of the Ising model and subsequently in the variance of the quenched disorder. This result is illustrated by some high-precision calculations of the free energy obtained by a straightforward numerical implementation of our sequential summation method.
Keywords
Cite
@article{arxiv.cond-mat/9910186,
title = {Summability of the perturbative expansion for a zero-dimensional disordered spin model},
author = {G. Alvarez and V. Martin-Mayor and J. J. Ruiz-Lorenzo},
journal= {arXiv preprint arXiv:cond-mat/9910186},
year = {2009}
}
Comments
LaTeX, 12 pages and 4 figures