Abstract
Let a<b, \(\Omega=[a,b]^{{\mathbb{Z}}^{d}}\) and H be the (formal) Hamiltonian defined on Ω by
where J:ℤd→ℝ is any summable non-negative symmetric function (J(x)≥0 for all x∈ℤd, ∑ x J(x)<∞ and J(x)=J(−x)). We prove that there is a unique Gibbs measure on Ω associated to H. The result is a consequence of the fact that the corresponding Gibbs sampler is attractive and has a unique invariant measure.
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Ferrari, P.A., Grynberg, S.P. No Phase Transition for Gaussian Fields with Bounded Spins. J Stat Phys 130, 195–202 (2008). https://doi.org/10.1007/s10955-007-9423-9
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DOI: https://doi.org/10.1007/s10955-007-9423-9