Fluctuations of the Phase Boundary in the Ising Ferromagnet
- Dobrushin, R.
- Hryniv, O.
2010 Mathematics Subject Classification
- 60F17 60F10 82B20 82B24
- Ising model, phase boundary, large deviations, invariance principle, conditional limit theorems, Wulff construction
We discuss statistical properties of phase boundary in the 2D low-temperature Ising ferromagnet in a box with the two-component boundary conditions. We prove the weak convergence in C [O, 1] of measures describing the fluctuations of phase boundaries in the canonical ensemble of interfaces with fixed endpoints and area enclosed below them. The limiting Gaussian measure coincides with the conditional distribution of certain Gaussian process obtained by the integral transformation of the white noise.
- Comm. Math. Phys., 189 (1997) pp. 395--445.