Amorphous Ferro- and Antiferromagnetism Within an RPA-CPA Theory

Abstract

We consider the system to be governed by a Heisenberg spin Hamiltonian with vanishing external field, i.e. u→0

$$H = A\sum\limits_{f,p} {J(f,p)} {S_f}.{S_p} - \mu \sum\limits_I {S_f^z} $$

(1)

Here A=−1 for the ferromagnetic case and +l for the antiferromagnetic case. The exchange integral between any site p and its surrounding shell of atoms (which we take to consist of z atoms on the average) is to be random with a probability distribution P(J) such that P(J) is zero outside the range J₂>J >J₁ and

$$\int\limits_{{J_1}}^{{J_2}} P \left( J \right)dJ = 1. $$

(2)

( Note that it is the fluctuations in the neighboring environment, in general, and in the separation vectors (f-p) as compared with the corresponding vectors for a crystalline lattice of coordination z , in particular, which cause these fluctuations in the exchange integral J(f,p).