Publication: Summability of the perturbative expansion for a zero-dimensional disordered spin model
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2000-02-11
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IOP Publishing
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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.
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© 2000 IOP Publishing Ltd. We thank Professors G. Parisi for useful discussions and A. J. Bray for providing references. The financial support of the Universidad Complutense under project PR156/97-7100, the Comisión Interministerial de Ciencia y Tecnología under project AEN96-1708, and a postdoctoral grant from the MEC are also gratefully acknowledged.