Macro–micro relations in dipolar orientational relaxation: An exactly solvable model of dielectric relaxation

The relationship between the microscopic orientational relaxation time (τm) and the collective, macroscopic relaxation time (τM) of a dipolar liquid has been a subject of considerable interest. We examine this relation for the kinetic Ising model of Glauber, used recently by Skinner to describe dielectric relaxation in glassy polymers. In this model, exact solutions for both the same spin and the collective spin time correlation functions are possible. We find that these two correlation functions are entirely different from each other. The self spin correlation function is highly nonexponential, as pointed out by Glauber and by Skinner. But, the collective spin relaxation is single exponential, and the wave vector and frequency dependent dielectric function is of simple Debye form. The reason for this difference is discussed.