Abstract.
We consider a ferromagnetic spin system with unbounded interactions on the d-dimensional integer lattice (d > 1). Under mild assumptions on the one-body interactions (so that arbitrarily deep double wells are allowed), we prove that if the coupling constants are small enough, then the finite volume Gibbs states satisfy the log-Sobolev inequality uniformly in the volume and the boundary condition.
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Received: 11 November 1997 / Revised version: 17 July 1998
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Yoshida, N. The log-Sobolev inequality for weakly coupled lattice fields. Probab Theory Relat Fields 115, 1–40 (1999). https://doi.org/10.1007/s004400050235
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DOI: https://doi.org/10.1007/s004400050235
- Key wordsMathematics Subject Classification (1991): 60K35, 82B20