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Paper   IPM / Physic / 9600
School of Physics
  Title:   Thermal Behavior of Spin Clusters and Interfaces in Two-Dimensional Ising Model on Square Lattice
  Author(s):  A.A. Saberi
  Status:   Published
  Journal: J.Stat. Mech: Theory and Experiments
  Year:  2009
  Pages:   P07030
  Supported by:  IPM
Extensive Monte Carlo study of two-dimensional Ising model is done to investigate the 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 square lattice with strip geometry and show that such definition is consistent with conformal invariant properties of interfaces at critical temperature, Tc. The effective fractal dimensions of spin clusters and interfaces (dc and dI, respectively) are obtained as a function of temperature. We find that the effective fractal dimension of the spin clusters behaves almost linearly with temperature in three different regimes. It is also found that the effective fractal dimension of the interfaces undergoes a sharp crossover around Tc, between values 1 and 1.75 at low and high temperatures, respectively. We also check the finite-size scaling hypothesis for the percolation probability and the average mass of the largest spin-cluster in a good agreement with the theoretical predictions.

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