Phase Transitions in Three Dimensional Ising Systems under Free and Periodic Boundary Conditions

摘要

The Ising model (and also the Ising model in a transverse field) has been used extensively to investigate ferroelectric phase transitions. Numerical Monte Carlo simulations of phase transitions in three-dimensional Ising systems with variable size (2 < = L < = 100) have been performed. The susceptibility maximum and peak temperature T~(3D)_c (L, L_(c)) for free and periodic boundary conditions have been determinated and have been observed to be well fitted by simple expressions as a function of L. For L - > infinity, as expected [T~(3D)_c] = [T~(3D)_c]_(pbc) being fbc = free boundary conditions and pbc= periodic boundary conditions. Scaling plots Ml~(beta/v) vs epsilonL~(l/v) for larger L with both boundary conditions were obteined and compared. The scaling function for our data up to L approx = 100 was examined closely and an excellent fit at T - > T_c was obtenied