Renormalization-group analysis of the critical dynamics of a Hamiltonian model with a scalar displacive transition

The dynamic critical behavior of a system of a coupled classical anharmonic oscillators having a displacive phase transition is discussed by renormalization-group methods, starting from the microscopic Hamiltonian of the system for dimension $d$ equal to or close to 4, and for a transition temperature close to zero. As a consequence of energy conservation, heat-diffusion poles are found in the renormalized vertex functions. The dynamic critical behavior of the system is shown to be equivalent to the stochastic model $C$ of Halperin, Hohenberg, and Ma, where the energy density was introduced as a separate conserved field. It is shown how to calculate the nonuniversal dynamic critical amplitudes in terms of the microscopic Hamiltonian of the model, which has been chosen such that all phonons can decay by three-phonon processes.