arXiv subjects
Publications and source records attributed to R. J. Messikh.
We study the behavior of the two-dimensional Ising model in a finite box at temperatures that are below, but very close to, the critical temperature. In a regime where the temperature approaches the critical point and, simultaneously, the size of the box grows fast enough, we establish a large deviation principle that proves the appearance of a round Wulff crystal.
For the two dimensional Ising model, we construct the adequate surface tension near criticality. The latter quantity has been shown to play a central role in the study of phase coexistence in a joint limit where the temperature approaches the critical point from below and simultaneously the size of the system increases fast enough.
By adapting the renormalization techniques of Pisztora, we establish surface order large deviations estimates for FK-percolation on $\Z^2$ with parameter $q\geq 1$ and for the corresponding Potts models. Our results are valid up to the exponential decay threshold of dual connectivities which is widely believed to agree with the critical point.