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Weak Mixing and Analyticity of the Pressure in the Ising Model

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Year 2019
Abstract We prove that the pressure (or free energy) of the finite range ferromagnetic Ising model on Z^d is analytic as a function of both the inverse temperature b and the magnetic field h whenever the model has the exponential weak mixing property. We also prove the exponential weak mixing property whenever h>=0. Together with known results on the regime h=0,b<b_c, this implies both analyticity and weak mixing in all the domain of (b,h) outside of the transition line [b_c,infinity)x{0}. The proof of analyticity uses a graphical representation of the Glauber dynamic due to Schonmann and cluster expansion. The proof of weak mixing uses the random cluster representation.
Keywords Ising ModelAnalyticityFree EnergyMixingGlauber DynamicCluster Expansion
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arXiv: 1905.12928
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OTT, Sébastien. Weak Mixing and Analyticity of the Pressure in the Ising Model. 2019. https://archive-ouverte.unige.ch/unige:121359

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Deposited on : 2019-07-29

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