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Upper Bounds on the Critical Temperature for Kac Potentials |
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| Authors: | M Cassandro R Marra E Presutti |
| Institution: | 1. Dipartimento di Fisica, Università di Roma La Sapienza, and Istituto Nazionale di Fisica della Materia, Sezione di Roma, 00185, Rome, Italy 2. Dipartimento di Fisica, Università di Roma Tor Vergata, 00133, Rome, Italy 3. Dipartimento di Matematica, Università di Roma Tor Vergata, 00133, Rome, Italy |
| Abstract: | We consider an Ising system in two dimensions with a two body ferromagnetic interaction J γ(x, y) that depends on the Kac scaling parameter γ. We prove that the inverse critical temperature βcr(γ) is strictly above the mean-field value (equal to 1), namely that there exists C>0 so that for any b<C, βcr(γ)> 1 + bγ2log γ?1 for all γ sufficiently small. The temperature shift Cγ2log γ?1 is to leading orders equal to the covariance of the magnetization fluctuations. |
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