On the saturation field of magnets

Three small comments on the saturation field for magnetization curves of magnets are noted. The saturation field is generally formulted for magnets with translational invariance, so that one can calculate the coupling constant J of magnets from magnetization measurements up to the saturating point. An upperbound for more general cases and an inequality for bipertite cases are obtained. It is shown that these two inequalities are reduced to an equality when the system satisfies some bipartite and homogeneity conditions.