WIAS Preprint No. 844, (2003)

On the Gibbs phase rule in the Pirogov-Sinai regime


  • Bovier, Anton
  • Merola, Immacolata
  • Presutti, Ericco
  • Zahradník, Miloš

2010 Mathematics Subject Classification

  • 82A25


  • Gibbs phase rule, Pirogov-Sinai theory, contour models, Kac-interactions




We consider extended Pirogov-Sinai models including lattice and continuum particle systems with Kac potentials. Calling λ an intensive variable conjugate to an extensive quantity α appearing in the Hamiltonian via the additive term -λα, we prove that if a Pirogov-Sinai phase transition with order parameter λ occurs at λ = 0, then this is the only point in an interval of values of λ centered at 0, where phase transitions occur.

Appeared in

  • J. Statist. Phys, 114 (2004), pp. 1235--1267

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