Measurement of the correlation length on Ising model

Abstract

We present a method for measuring the correlation length of the Ising model. Starting from a ground state, we consider a quantity K(t, T) L(< M-2(t)>/< M(t)>(2) - 1)(1/d) where M(t), L and d denote the magnetization, the system size, and substrate dimension of the model, respectively. K(t, T) follows a power-law behavior K(t, T-c) similar to t(1/z) at the critical temperature T-c and the saturation value of K(infinity, T) shows that K-sat (T) similar to vertical bar T-c - T vertical bar(-v). The critical exponents v = 1.00(1) and z = 2.15(1) are estimated in a two dimensional square lattice. By calculating solely K(t, T), we could obtain the correlation-length exponent directly. Also, the correlation length and critical exponents of the three dimensional Ising model on a cubic lattice are discussed. We believe that this is an effective method, which can be feasibly applied to various spin models.