2008/12/31 by Giuseppe Genovese, Adriano Barra · 1 citation
Physics and Astronomy · Mathematics · #math-ph #math.MP
paper · pdf · doi:10.1063/1.3131687
published as J. Math. Phys. 2009
arxiv created 2009/05/07 · arxiv updated 2015/05/12
Inspired by the bridge pioneered by Guerra among statistical mechanics on lattice and analytical mechanics on 1+1 continuous Euclidean space-time, we built a self-consistent method to solve for the thermodynamics of mean-field models defined on lattice, whose order parameters self average. We show the whole procedure by analyzing in full details the simplest test case, namely the Curie-Weiss model. Further we report some applications also to models whose order parameters do not self-average, by using the Sherrington-Kirkpatrick spin glass as a guide.