By Barry M McCoy

Statistical Mechanics is the learn of platforms the place the variety of interacting debris turns into limitless. within the final fifty years great advances were made that have required the discovery of fullyyt new fields of arithmetic equivalent to quantum teams and affine Lie algebras. they've got engendered extraordinary discoveries pertaining to non-linear differential equations and algebraic geometry, and feature produced profound insights in either condensed topic physics and quantum box concept. regrettably, none of those advances are taught in graduate classes in statistical mechanics. This publication is an try to right this challenge. It starts off with theorems at the lifestyles (and lack) of order for crystals and magnets and with the idea of serious phenomena, and keeps through proposing the tools and result of fifty years of analytic and machine computations of section transitions. It concludes with an in depth presentation of 4 of crucial of precisely solved difficulties: the Ising, eight vertex, challenging hexagon and chiral Potts versions.