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arXiv · 0712.0312

Mean-field behavior for long- and finite range Ising model, percolation and self-avoiding walk

Markus Heydenreich·Remco van der Hofstad·Akira Sakai
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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 $d>2(α\wedge2)$ for self-avoiding walk and the Ising model, and $d>3(α\wedge2)$ 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. (2007)

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Markus Heydenreich, Remco van der Hofstad, Akira Sakai. 2008-05-29. Mean-field behavior for long- and finite range Ising model, percolation and self-avoiding walk. https://doi.org/10.1007/s10955-008-9580-5

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