Abstract

Intermediate Fluctuations in the Ising Model S. Ott, S. Shlosman, Y. Velenik Markov Process. Related Fields 30, 97-104 (2024). 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 $N^b$, $1/3 \leq b \leq 1/2$, depending on the location on the interface. We state a conjecture concerning the locations where the fluctuations are of the order $N^b$. Key words: Ising model, interface, fluctuations Files: Published version, bibtex