Dynamical Plane Rotator Model. II. Dynamical Correlation Functions in Molecular Field Approximation

Abstract

Dynamical correlation functions S ( q , ω)'s are obtained by the use of molecular field approximation for the dynamical plane rotator model: H =∑ N i =1 p 2 i /2 I +∑ i < j J i j (1-cos ( Q i - Q j )). Our results are exact in the limit of long range interaction where J i j is always J / N and in the limit of infinite N . Below the critical point T c , S ( q , ω)'s have two peaks corresponding to phonon excitation and sometimes a central peak at ω=0. Above T c , however, they have only a central peak at ω=0. At T = T c –, phenomena of critical slowing down are observed.