Non-Analyticity and the van der Waals Limit

2003/02/24 by S. Friedli, Sacha Friedli, C.-E. Pfister +1 · 1 citation
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Quantum Mechanics and Applications #Statistical Mechanics and Entropy #cond-mat.stat-mech

paper · pdf · doi:10.1023/b:joss.0000012506.98828.dd

arxiv created 2003/02/24 · openalex publication_date 2004/01/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the analyticity properties of the free energy f_\ga(m) of the Kac model at points of first order phase transition, in the van der Waals limit \ga\searrow 0. We show that there exists an inverse temperature β₀ and \ga₀>0 such that for all β≥ β₀ and for all \ga∈(0,\ga₀), f_\ga(m) has no analytic continuation along the path m\searrow m^* (m^* denotes spontaneous magnetization). The proof consists in studying high order derivatives of the pressure p_\ga(h), which is related to the free energy f_\ga(m) by a Legendre transform.

Citations

• Liquid-Vapor Phase Transitions for Systems with Finite Range Interactions
• On the van der Waals Theory of the Vapor-Liquid Equilibrium. I. Discussion of a One-Dimensional Model
• On the Singularity of the Free Energy at First Order Phase Transition

Cited by

• Rigorous Analysis of Singularities and Absence of Analytic Continuation at First-Order Phase-Transition Points in Lattice-Spin Models