Spin-dynamics simulations of the triangular antiferromagnetic XY model

Abstract

Using Monte Carlo and spin-dynamics methods, we have investigated the dynamic behavior of the classical, antiferromagnetic XY model on a triangular lattice with linear sizes $L \leq 300$. The temporal evolutions of spin configurations were obtained by solving numerically the coupled equations of motion for each spin using fourth-order Suzuki-Trotter decompositions of exponential operators. From space- and time-displaced spin-spin correlation functions and their space-time Fourier transforms we obtained the dynamic structure factor $S({\bf q},w)$ for momentum ${\bf q}$ and frequency $\omega$. Below $T_{KT}$(Kosterlitz-Thouless transition), both the in-plane ($S^{xx}$) and the out-of-plane ($S^{zz}$) components of $S({\bf q},\omega)$ exhibit very strong and sharp spin-wave peaks. Well above $T_{KT}$, $S^{xx}$ and $S^{zz}$ apparently display a central peak, and spin-wave signatures are still seen in $S^{zz}$. In addition, we also observed an almost dispersionless domain-wall peak at high $\omega$ below $T_{c}$(Ising transition), where long-range order appears in the staggered chirality. Above $T_{c}$, the domain-wall peak disappears for all $q$. The lineshape of these peaks is captured reasonably well by a Lorentzian form. Using a dynamic finite-size scaling theory, we determined the dynamic critical exponent $z$ = 1.002(3). We found that our results demonstrate the consistency of the dynamic finite-size scaling theory for the characteristic frequeny $\omega_{m}$ and the dynamic structure factor $S({\bf q},\omega)$ itself.