WIAS Preprint No. 240, (1996)

The Low-Temperature Phase of Kac-Ising Models


  • Bovier, Anton
  • Zahradník, Miloš

2010 Mathematics Subject Classification

  • 60K35 82B20 82B26


  • Ising models, Kac potentials, low temperature Gibbs states, contours, Peierls argument




We analyse the low temperature phase of ferromagnetic Kac-Ising models in dimensions d ≥ 2. We show that if the range of interactions is γ-1, then two disjoint translation invariant Gibbs states exist, if the inverse temperature β satisfies β - 1 ≥ γκ, where κ = d(1-ε) ⁄ (2d+2)(d+1), for any ε > 0. The prove involves the blocking procedure usual for Kac models and also a contour representation for the resulting long-range (almost) continuous spin system which is suitable for the use of a variant of the Peierls argument.

Appeared in

  • J. Statist. Phys. 87 (1997) pp. 311-333

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