Lace expansion for the Ising model

Details Lace expansion for the Ising model Lace expansion for the Ising model

2005-10-29

arxiv.org/abs/math-ph/0510093v2

Physics

Mathematical Physics

54 pages, 12 figures

Scientific paper

The lace expansion has been a powerful tool for investigating mean-field behavior for various stochastic-geometrical models, such as self-avoiding walk and percolation, above their respective upper-critical dimension. In this paper, we prove the lace expansion for the Ising model that is valid for any spin-spin coupling. For the ferromagnetic case, we also prove that the expansion coefficients obey certain diagrammatic bounds that are similar to the diagrammatic bounds on the lace-expansion coefficients for self-avoiding walk. As a result, we obtain Gaussian asymptotics of the critical two-point function for the nearest-neighbor model with d>>4 and for the spread-out model with d>4 and L>>1, without assuming reflection positivity.

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