Existence and uniqueness of equilibrium states for some spin and continuum systems |
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| Authors: | M Cassandro G Gallavotti J L Lebowitz J L Monroe |
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| Institution: | (1) Istituto di Fisica, Università di Roma, Rome, Italy;(2) Istituto Nazionale di Fisica Nucleare — Sezione di Roma, Italy;(3) Istituto di Fisica Teorica — Università di Napoli, Italy;(4) Belfer Graduate School of Science, Yeshiva University, New York, N.Y., USA;(5) Dept. of Physics Columbia University, New York, N.Y., USA |
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| 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 ferromagnetis 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 ofA –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.Supported in part by Air Force Grant n. 732430. |
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