**Authors**:
M.Cassandro,G.Gallavotti,J.L.Lebowitz,E.Monroe

**Title**:
*Exitence and uniqueness of equilibrium
states for some spin and continoum systems*

Communication in Mathematical Physics, **32**, 153--165, 1973,

**Abstract:** The one to one correspondence
between the existence of a unique equilibrium state and the
differentiability of the free energy density with respect to the
external field previously shown for Ising ferromagnets is extendend to
higher valued spin systems as well as to continuum systems satisfying
the Fortuin, Kasteleyn and Ginibre inequalities. In particular this is
shown to hold for a mixture of A B particles in which there is no
interaction between like particles and a repulsion between unlike
particles. Where the derivative of the free energy is discontinuous
there are at least two equilibrium states.

**Key words: **
Statistical Mechanics, Phase Rule, Phase Transitions,
Thermodynamic Limit, Lattice Gas

Giovanni Gallavotti

Fisica, Universita' di Roma 1

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