On the Existence of Spontaneous Polarization at Finite Temperature in Infinite Ising Strips

Abstract

Monte Carlo data for ferroelectric Ising strips of width D = 8, 16, 32, 64 and L = 1000, 2000, 5000, 10.000 show that the spontaneous polarization is non-zero at temperatures below

being D∗ = 4.2695…. This means that the effective number of nearest neighbours n _eff = {1−1/2D}/4(D) for Ising strips with D > D∗ implies an effective dimensionality d _eff (D) intermediate between d _eff (D∗) = 3/2, (at which T _c (D∗) = 0), and d _eff (∞) = 2, (at which T _c (∞) = 2.2691).