Mean-Field Behavior for Long- and Finite Range Ising Model,Percolation and Self-Avoiding Walk |
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| Authors: | Markus Heydenreich Remco van der Hofstad Akira Sakai |
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| Institution: | (1) Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600, MB, Eindhoven, The Netherlands;(2) Creative Research Initiative “Sousei”, Hokkaido University, North 21, West 10, Kita-ku, Sapporo 001-0021, Japan |
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| Abstract: | We consider self-avoiding walk, percolation and the Ising model with long and finite range. By means of the lace expansion
we prove mean-field behavior for these models if d>2(α
∧2) for self-avoiding walk and the Ising model, and d>3(α
∧2) for percolation, where d denotes the dimension and α the power-law decay exponent of the coupling function. We provide a simplified analysis of the lace expansion based on the
trigonometric approach in Borgs et al. (Ann. Probab. 33(5):1886–1944, 2005).
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| Keywords: | Lace expansion Ising model Percolation Self-avoiding walk Critical exponent Mean-field behavior |
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