Abstract
An extensive Monte Carlo study of the two-dimensional Ising model is made to investigatethe statistical behavior of spin clusters and interfaces as a function of temperature,T. We use a tie-breaking rule to define interfaces of spin clusters on a squarelattice with strip geometry and show that such definitions are consistent withconformally invariant properties of interfaces at the critical temperature,Tc. The effective fractal dimensions of spin clusters and interfaces (dc anddI, respectively) are obtained as a function of temperature. We find that theeffective fractal dimension of the spin clusters varies almost linearly withtemperature in three different regimes. It is also found that the effectivefractal dimension of the interfaces undergoes a sharp crossover aroundTc, betweenthe values 1 and 1.75 at low and high temperatures, respectively. We also check the finite-size scaling hypothesisfor the percolation probability, and the average mass of the largest spin cluster is in a goodagreement with the theoretical predictions.
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