Measurement of the correlation length on Ising model

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) ∼ t^1/z at the critical temperature T_c and the saturation value of K(∞ , T) shows that K_sat (T) ∼ |T_c - T|^-ν . The critical exponents ν = 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.