Julia Sets and Complex Singularities of Free Energies (Memoirs of the American Mathematical Society; Volume 234, Number 1102) by Jianyong Qiao - 2014

American Mathematical Society, 2014. Paperback. New Book. Paperback. Part of the Memoirs of the American Mathematical Society series, this volume seeks to prove that unstable sets, or "Julia sets," are a set of complex singularities of free energy in statistical mechanics when treated as a complex dynamical system. The book begins with an abstract and introduction and then includes five chapters that elaborate on the details of this idea. Topics covered include Potts models, dynamic complexity of renormalization transformations, the connectivity of Julia sets, Jordan domains, Fatou components and the critical exponent of free energy. (2014 Ringgold, Inc., Portland, OR)