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.

arXiv comment8 pages, 8 figures; v2: minor changes in text, various plots are put in one figure

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• Geometrical vs. Fortuin-Kasteleyn Clusters in the Two-Dimensional $q$-State Potts Model
• Conformal Fractal Geometry and Boundary Quantum Gravity
• Fractal geometry of critical Potts clusters
• Site Percolation and Phase Transitions in Two Dimensions

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