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(αâ§2) for self-avoiding walk and the Ising
model, and d>3(αâ§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. (2007)Comment: 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