Summability of the perturbative expansion for a zero-dimensional disordered spin model
arXiv:cond-mat/9910186 · doi:10.1088/0305-4470/33/5/302
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.
LaTeX, 12 pages and 4 figures