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 $la$ an intensive variable conjugate to an extensive quantity $al$ appearing in the Hamiltonian via the additive term $-laal$, we prove that if a Pirogov-Sinai phase transition with order parameter $al$ occurs at $la=0$, then this is the only point in an interval of values of $la$ centered at 0, where phase transitions occur.

Appeared in

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

Download Documents