Critical Relaxation in Dipolar Ising Model at Marginal Dimension

Abstract

The equation of motion for a dipolar Ising Model at a marginal dimension d = 3 is studied on the basis of the renormalized field theory. It is shown that the temperature dependence of a nonlinear relaxation time t ( n l ) is related to a linear one t ( l ) as t ( n l ) = t ( l ) M s + , where M s + is defined as the spontaneous magnetization at the temperature T c -|τ| irrespective of the sign of the renormalized temperature difference τ= T - T c .