Summability of the perturbative expansion for a zero-dimensional disordered spin model

Details Summability of the perturbative expansion for a zero-dimensional disordered spin model Summability of the perturbative expansion for a zero-dimensional disordered spin model

1999-10-13

arxiv.org/abs/cond-mat/9910186v1

J. Phys. A 33, 841 (2000)

Physics

Condensed Matter

Statistical Mechanics

LaTeX, 12 pages and 4 figures

Scientific paper

10.1088/0305-4470/33/5/302

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.

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