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