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

M.O. Heydenreich, R.W. Hofstad, van der, A. Sakai

Research output: Contribution to journalArticleAcademicpeer-review

36 Citations (Scopus)

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(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).
Original languageEnglish
Pages (from-to)1001-1049
JournalJournal of Statistical Physics
Volume132
Issue number6
DOIs
Publication statusPublished - 2008

Fingerprint Dive into the research topics of 'Mean-field behavior for long- and finite-range Ising model, percolation and self-avoiding walk'. Together they form a unique fingerprint.

Cite this