We consider extended Pirogov - Sinai models including lattice and continuum particle systems with Kac potentials. Call lambda an intensive variable conjugate to an extensive quantity alpha appearing in the Hamiltonian via the additive term - lambdaalpha. We suppose that a Pirogov - Sinai phase transition with order parameter alpha occurs at lambda = 0, and that there are two distinct classes of DLR measures, the plus and the minus DLR measures, with the expectation of a respectively positive and negative in the two classes. We then prove that lambda = 0 is the only point in an interval I of values of lambda centered at 0 where this occurs, namely the expected value of alpha is positive, respectively negative, in all translational invariant DLR measures at {lambda > 0} I and {lambda < 0} I.
Bovier, A., Merola, I., Presutti, E., Zahradnik, M. (2004). On the Gibbs phase rule in the Pirogov-Sinai regime. JOURNAL OF STATISTICAL PHYSICS, 114, 1235-1267 [10.1016/j.ejc.2003.10.011].
On the Gibbs phase rule in the Pirogov-Sinai regime
PRESUTTI, ERRICO;
2004-01-01
Abstract
We consider extended Pirogov - Sinai models including lattice and continuum particle systems with Kac potentials. Call lambda an intensive variable conjugate to an extensive quantity alpha appearing in the Hamiltonian via the additive term - lambdaalpha. We suppose that a Pirogov - Sinai phase transition with order parameter alpha occurs at lambda = 0, and that there are two distinct classes of DLR measures, the plus and the minus DLR measures, with the expectation of a respectively positive and negative in the two classes. We then prove that lambda = 0 is the only point in an interval I of values of lambda centered at 0 where this occurs, namely the expected value of alpha is positive, respectively negative, in all translational invariant DLR measures at {lambda > 0} I and {lambda < 0} I.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
