Thickness Dependence of Effective Critical Exponents in Three-Dimensional Ising Plates

Abstract

Phase transitions in 'sing plates of equal area and different thicknesses have been studied by the Monte Carlo approach. The evolution of the critical temperature and of the effective critical exponents with the thickness of the lattice has been numerically determined. The thickness dependence of the maximum value of the effective critical exponents is well described by an exponential decay towards the respective three-dimensional value.

Numerical approach to phase transitions in nanoscopic layered systems

“…These authors find that the critical exponents for the surface are different from those for the bulk. Scaling, multicritical points, and crossover have also been studied as the surface interaction changes with respect to the bulk interaction [1].The evolution of the effective critical exponents with temperature has been studied in the close vicinity of T c for systems with thin-film geometry and with free surfaces by means of series expansion [3], the renormalization group [4] and high-accuracy Monte Carlo calculations, in Ising systems [5][6][7][8] and in the X-Y model [9]. Attention was given to the study of the crossover phenomena in the effective critical exponents from three-to two-dimensional as the system approaches the critical temperature.…”

“…For a certain temperature depending on the film thickness the system notes that it belongs to the twodimensional universality class and it starts the crossover by means of a decrease towards the two-dimensional value. Note that between these two zones the system reaches a maximum (β m ) at t = t cr which we may use to characterize the film thickness [7]. Normally, due to the finite value of the surface, the system cannot reach the two-dimensional value and the crossover zone is eventually interrupted by finite-size effects.…”