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On the 2D Ising Wulff crystal near criticality. (English) Zbl 1185.82010

Summary: 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.

MSC:

82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
60F10 Large deviations
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B27 Critical phenomena in equilibrium statistical mechanics
82B26 Phase transitions (general) in equilibrium statistical mechanics
82D25 Statistical mechanics of crystals
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