Correlation inequalities and uniqueness of the equilibrium state for the plane rotator ferromagnetic model |
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Authors: | A Messager S Miracle-Sole C Pfister |
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Institution: | 1. Centre de Physique Théorique, CNRS, F-13274, Marseille, France
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Abstract: | We derive new inequalities for the plane rotator ferromagnetic model and use them to obtain the following results: - If the model is isotropic, the derivability of the free energy as function of the magnetic fieldh implies the existence of a unique translation invariant Gibbs state and if furthermoreh=0 all Gibbs states are invariant by rotation of the spins.
- If the model is anisotropic the above assertion holds forh non-zero.
- If the model is anisotropic then there are at most two extremal translation invariant Gibbs states for almost all values of the anisotropy parameter.
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