Theorem on the origin of phase transitions

Year: 2004

Authors: Franzosi R., Pettini M.

Autors Affiliation: Dipartimento di Fisica, Università di Pisa, I.N.F.N., Sezione di Pisa, and I.N.F.M., Unità di Pisa, via Buonarroti 2, I-56127 Pisa, Italy; Istituto Nazionale di Astrofisica, Largo E. Fermi 5, 50125 Firenze, I.N.F.M., Unità di Firenze, and I.N.F.N., Sezione di Firenze, Italy

Abstract: 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 Sigma(v)={(q(1),…,q(N))is an element ofR(N)\\V(q(1),…,q(N))=v}, vis an element ofR, change topology at some v(c) in a given interval [v(0),v(1)] of values v of V, the Helmoltz free energy must be at least twice differentiable in the corresponding interval of inverse temperature (beta(v(0)),beta(v(1))) also in the N–>infinity limit. Thus, the occurrence of a phase transition at some beta(c)=beta(v(c)) is necessarily the consequence of the loss of diffeomorphicity among the {Sigma(v)}(vvc), which is the consequence of the existence of critical points of V on Sigma(v=vc), that is, points where delV=0.

Journal/Review: PHYSICAL REVIEW LETTERS

Volume: 92 (6)      Pages from: 060601-1  to: 060601-4

KeyWords: Diffeomorphicity; Helmoltz free energy; Legendre transforms; Wave numbers, Computer simulation; Degrees of freedom (mechanics); Differentiation (calculus); Free energy; Hamiltonians; Kinetic energy; Lyapunov methods; Markov processes; Matrix algebra; Monte Carlo methods; Probability density function; Thermodynamics, Phase transitions
DOI: 10.1103/PhysRevLett.92.060601

Citations: 96
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