TY - JOUR
T1 - Mean-field behavior for long- and finite-range Ising model, percolation and self-avoiding walk
AU - Heydenreich, M.O.
AU - Hofstad, van der, R.W.
AU - Sakai, A.
PY - 2008
Y1 - 2008
N2 - 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(a ¿2) for self-avoiding walk and the Ising model, and d>3(a ¿2) for percolation, where d denotes the dimension and a 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).
AB - 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(a ¿2) for self-avoiding walk and the Ising model, and d>3(a ¿2) for percolation, where d denotes the dimension and a 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).
U2 - 10.1007/s10955-008-9580-5
DO - 10.1007/s10955-008-9580-5
M3 - Article
SN - 0022-4715
VL - 132
SP - 1001
EP - 1049
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 6
ER -