2003/12/15 by Roberto Franzosi, Marco Pettini · 2 citations
Materials Science · Mathematics · Physics and Astronomy · #Material Dynamics and Properties #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #cond-mat.stat-mech #math-ph #math.MP
paper · pdf · doi:10.1103/physrevlett.92.060601
published as Phys.Rev.Lett., 92, 60601, (2004) · 10 pages, Statistical Mechanics, Phase Transitions, General Theory. Phys. Rev. Lett., in press
arxiv created 2003/12/15 · openalex publication_date 2004/02/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For physical systems described by smooth, finite-range, and confining microscopic interaction potentials V with continuously varying coordinates, we announce and outline the proof of a theorem that establishes that, unless the equipotential hypersurfaces of configuration space \ensuremathΣv=(q1,…,qN)\ensuremath∈ℝN|V(q1,…,qN)=v, v\ensuremath∈ℝ, change topology at some vc in a given interval [v0,v1] of values v of V, the Helmoltz free energy must be at least twice differentiable in the corresponding interval of inverse temperature (\ensuremathβ(v0),\ensuremathβ(v1)) also in the N\ensuremath→\ensuremath∞ limit. Thus, the occurrence of a phase transition at some \ensuremathβc=\ensuremathβ(vc) is necessarily the consequence of the loss of diffeomorphicity among the \ensuremathΣv_v<vc and the \ensuremathΣv_v>vc, which is the consequence of the existence of critical points of V on \ensuremathΣ_v=vc, that is, points where \ensuremath∇V=0.