2003/05/20 by Sacha Friedli, Charles-Édouard Pfister, C. E. Pfister
Physics and Astronomy · #Quantum many-body systems #Statistical Mechanics and Entropy #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevlett.92.015702
4 pages, 2 figures
arxiv created 2003/05/20 · openalex publication_date 2004/01/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We report about two new rigorous results on the nonanalytic properties of thermodynamic potentials at first-order phase transition. For lattice models (d\ensuremath≥2) with arbitrary finite state space, finite-range interactions which have two ground states, we prove that the pressure has no analytic continuation at the first-order phase-transition point, under the only further assumptions that the Peierls condition is satisfied for the ground states and that the temperature is sufficiently low. For Ising models with Kac potentials J_\ensuremathγ(x)=\ensuremathγd\ensuremathφ(\ensuremathγx), where 0<\ensuremathγ<1 is a small scaling parameter, and \ensuremathφ a fixed finite-range potential, we relate the nonanalytic behavior of the pressure at the transition point to the range of interaction, which equals \ensuremathγ^\ensuremath-1. Our analysis exhibits a crossover between the nonanalytic behavior of finite-range models (\ensuremathγ>0) and analyticity in the mean field limit (\ensuremathγ\ensuremath\searrow0).