2005/06/24 by Ingo Hahn, Michael Kästner, Michael Kastner
Economics, Econometrics and Finance · Engineering · Mathematics · Physics and Astronomy · #Algorithm #Complex Systems and Time Series Analysis #Fluid Dynamics and Turbulent Flows #Mathematics #Statistical Mechanics and Entropy #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.72.056134
published as Phys.Rev. E72 (2005) 056134 · 10 pages, 5 figures
arxiv created 2005/06/24 · openalex publication_date 2005/11/29 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
A large deviation technique is applied to the mean-field model Phi4, providing an exact expression for the configurational entropy s(v,m) as a function of the potential energy v and the magnetization m. Although a continuous phase transition occurs at some critical energy vc, the entropy is found to be a real analytic function in both arguments, and it is only the maximization over m which gives rise to a nonanalyticity in s(v)=supm s(v,m). This mechanism of nonanalyticity-generation by maximization over one variable of a real analytic entropy function is restricted to systems with long-range interactions and has--for continuous phase transitions--the generic occurrence of classical critical exponents as an immediate consequence. Furthermore, this mechanism can provide an explanation why, contradictory to the so-called topological hypothesis, the phase transition in the mean-field model need not be accompanied by a topology change in the family of constant-energy submanifolds.