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



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Álvarez, Gabriel and Martín Mayor, Víctor and Ruiz Lorenzo, Juan J. (2000) Summability of the perturbative expansion for a zero-dimensional disordered spin model. Journal of physics A: mathematical and general, 33 (5). pp. 841-850. ISSN 0305-4470

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Official URL: http://dx.doi.org/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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© 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.

Uncontrolled Keywords:Dilute ising-model; Systems.
Subjects:Sciences > Physics > Physics-Mathematical models
ID Code:46811
Deposited On:19 Apr 2018 11:41
Last Modified:19 Apr 2018 11:51

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