TABLE OF CONTENTS A ferromagnet is a material that has a spontaneous magnetic moment even in zero field. We shall see that it is the simplest system exhibiting a second order phase transition. Our model of the ferromagnet is based on that of Weiss. [5] We first consider a collection of independent spin 1/2 elementary magnets (spins), each with magnetic moment ?. We discussed this system in Chapters 3 and 5, and found it to be a paramagnet. In a magnetic field B at temperature T, the magnetization (magnetic moment per unit volume), which is the vector sum of all the spins, is 
where n is the number of spins per unit volume and 
is the average moment per atom, projected on the direction of the applied magnetic field B. This average is, from Equation (5.46),
(see Example 5.5 and Problem 5.3). Here, as always, 
.
Our model of a ferromagnet starts with the same collection of spins, but assumes that there is an interaction between them, so that the energy of a spin depends on its direction relative to the directions of neighboring spins. [6] In the Weiss model this interaction is represented by a molecular (or internal) magnetic field, which is assumed to be proportional to the magnetization m, where 
. Thus, each elementary magnet is assumed to behave as if it were subject to a magnetic field B i nt=
