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

TL;DR

This paper numerically investigates the fractal structures of spin clusters and domain walls in the 2D Ising model at criticality, providing precise estimates that align with theoretical predictions.

Contribution

It offers improved numerical estimates of fractal dimensions of spin clusters and domain walls in the 2D Ising model, confirming theoretical predictions.

Findings

Fractal dimensions match theoretical values

Enhanced precision over previous numerical estimates

Numerical results support critical behavior theories

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.