Equilibrium dynamics of the sine-Gordon chain: A molecular-dynamics study

Abstract

Results of a molecular-dynamics study of the discrete sine-Gordon (SG) chain are reported, emphasizing $\phi -\phi$, $sin\phi -sin\phi$, and $cos\phi -cos\phi$ dynamic correlation functions ($\phi$ is the SG field variable). Correlations at the temperature $k_{B}T\simeq 0.29E_K$ ($E_K$ is the continuum SG kink-soliton energy) are interpreted in terms of elementary linear and nonlinear modes—kinks, breathers, single-, and multiphonons. The validity of "ideal-gas" approximations is assessed and corrections from lattice discreteness and mode-mode interactions are discussed. Finally, the relevance of our results to planar ferromagnetic chains (e.g., CsNi${\mathrm{F}}_3$) in an easy-plane applied magnetic field is assessed.