Fractal Structure of Spin Clusters and Domain Walls in 2D Ising Model

Abstract

The fractal structure of spin clusters and their boundaries in the critical two-dimensional (2D) Ising model is investigated numerically. The fractal dimensions of these geometrical objects are estimated by means of Monte Carlo simulations on relatively small lattices through standard finite-size scaling. The obtained results are in excellent agreement with theoretical predictions and partly provide significant improvements in precision over existing numerical estimates.

8 pages, 8 figures; v2: minor changes in text, various plots are put in one figure