Intermediate fluctuations in the Ising model. (English) Zbl 07912842
Summary: We study the fluctuations of the boundary of a large droplet of one phase of the low-T 2D Ising model in a \(N\times N\) box. It is known that these fluctuations are of the order of \(N^{(1/3)}\) in the vicinity of the walls, and of the order of \(N^{(1/2)}\) far away from the walls. We argue that in fact the fluctuations of this interface can be of any order \(N^b\), \(1/3\Leftarrow b\Leftarrow 1/2\), depending on the location on the interface. We state a conjecture concerning the locations where the fluctuations are of the order \(N^b\).
MSC:
60K35 | Interacting random processes; statistical mechanics type models; percolation theory |
82B26 | Phase transitions (general) in equilibrium statistical mechanics |
82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
60J10 | Markov chains (discrete-time Markov processes on discrete state spaces) |