Thermal Behavior of Spin Clusters and Interfaces in two-dimensional Ising Model on Square Lattice

摘要

Extensive Monte Carlo study of two-dimensional Ising model is done toinvestigate the statistical behavior of spin clusters and interfaces as afunction of temperature, $T$. We use a \emph{tie-breaking} rule to defineinterfaces of spin clusters on square lattice with strip geometry and show thatsuch definition is consistent with conformal invariant properties of interfacesat critical temperature, $T_c$. The \emph{effective} fractal dimensions of spinclusters and interfaces ($d_c$ and $d_I$, respectively) are obtained as afunction of temperature. We find that the effective fractal dimension of thespin clusters behaves almost linearly with temperature in three differentregimes. It is also found that the effective fractal dimension of theinterfaces undergoes a sharp crossover around $T_c$, between values 1 and 1.75at low and high temperatures, respectively. We also check the finite-sizescaling hypothesis for the percolation probability and the average mass of thelargest spin-cluster in a good agreement with the theoretical predictions.