The Shift Exponent of the Layered Square-Lattice Ising Models

Abstract

Layered square-lattice ferromagnetic Ising models (∞×∞× n lattices) are studied by the Monte Carlo simulation with the periodic boundary condition( n = 3 ∼8) and with the free boundary condition ( n = 4 ∼14) in the n -direction. The results show the dimensionality crossover from the square-lattice Ising model to the simple-cubic Ising model. The shift exponent λ shows the size dependent behavior contrary to the previous results, and goes to about λ∼1.60 in the limit, n → ∞, for both boundary conditions, which is consistent with λ= 1/ ν 3d .