Critical Coarsening Dynamics Of Spins =1/2, 3/2 Antiferromagnetic Ising Model On Triangular Lattice

The critical coarsening dynamics of the spinS =1/2, 3/2 antiferromagnetic Ising model on a triangular lattice is studied by the dynamic Monte Carlo simulation using a heat bath algorithm. The triangular antiferromagnetic Ising (TAI) model possesses an intrinsic geometrical frustration and a large degeneracy of ground state which may affect the equilibrium and non-equilibrium critical behaviors. TheS =1/2TAI has no phase transition at a finite temperature, but it was suggested that theS =3/2TAI has the Kosterlitz–Thouless (KT)-type phase transition at a finite temperature. We employ a finite size scaling approach for the correlation function from the short-time dynamics of theS =1/2, 3/2 TAI to calculate the values of the static critical exponent η and the dynamic exponentz. For theS =1/2TAI, our dynamic scaling analysis providesη =0.498±0.006andz =2.278±0.020atT =0, agreeing with the previous results. For theS =3/2TAI, after identifying a KT-transition temperatureTKT=0.51±0.01, we find the temperature-dependent η ranging from0.301±0.008atT =0.51to0.224±0.016atT =0along the KT-line whereas the value ofz =2.20±0.06is constant forT≤TKT. It is shown that the spinS =3/2TAI model and the two-dimensional XY model, sharing the KT-type phase transition, exhibit similar static critical and coarsening dynamics behavior. For both theS =1/2, 3/2 TAI, the value ofz (η)is compatible with (larger than) that of the Ising model atTcand the XY model forT≤TKTin two-dimension. Our results imply that although the quasi-long-range order disappears withηXY=0in the two-dimensional XY model atT =0, theS =3/2TAI still maintains it withηTAI=0.224due to the effect of a frustration and a high degeneracy of ground state.