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

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 $d>2(\alpha \wedge 2)$ for self-avoiding walk and the Ising model, and $d>3(\alpha \wedge 2)$ for percolation, where $d$ denotes the dimension and $\alpha$ 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)

43 pages, many figures. Version v2 with various (minor) changes (in particular in Sections 1.4 and A.1), and Sect. 4 is shortened. Journal of Statistical Physics (to appear)

References in corpus (1)

• Mean-field driven first-order phase transitions in systems with long-range interactions