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

Abstract

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 Tc 3D(L,Lc) 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 → ∞, as expected [Tc 3D]fbc = [Tc 3D]pbc being fbc = free boundary conditions and pbc = periodic boundary conditions. Scaling plots MLβ/v vs |ϵ|Ll/v for larger L with both boundary conditions were obteined and compared. The scaling function for our data up to L ≈ 100 was examined closely and an excellent fit at T → Tc was obtenied.