where M = ^^ pi is the total instantaneous dipole moment of the spherical i volume V, the vector sum of the individual dipoles pi, and it is dotted into the unit vector pointing in the direction of Eeff. The angled brackets denote the statistical thermodynamic average and the derivative is evaluated at zero field strength. Note that the pi have the magnitude of the dipole moments in a theoretical "gas" phase. A relationship between the thermal fluctuation term can be derived from statistical mechanics and one finally arrives  at:
Was this article helpful?