Short-Range Magnetic Order in a Modified Weiss Molecular-Field Theory

The fact that two different expressions for the isothermal susceptibility ${\chi }_T$ can be obtained within the framework of the Weiss molecular-field theory of ferromagnetism (WMFT) is discussed. We conclude that it is inconsistent within the WMFT to assume no spin correlation in treating two-spin correlation functions. The requirement that the two methods for computing ${\chi }_T$ give identical expressions provides a measure of the spin correlations. A second consistency condition is also imposed. These, together with the Weiss theory for single-spin averages, do not completely determine a modified theory, except at high temperature, where the resulting expressions for short-range order and specific heat are asymptotically correct. No further conditions or constraints have been uncovered, so that an ad hoc assumption is required to complete the theory for all temperatures and magnetic fields. Several simple assumptions give respectable short-range order and specific-heat curves. The theory is essentially a Weiss theory, modified so as to be consistent when forming two-spin averages.