Critical coarsening dynamics of spin S = 1/2, 3/2 antiferromagnetic ising model on triangular lattice

The critical coarsening dynamics of the spin S = 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 antiferromagnetie 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. The S = 1/2 TAI has no phase transition at a finite temperature, but it was suggested that the S = 3/2 TAI 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 the S = 1/2, 3/2 TAI to calculate the values of the static critical exponent η and the dynamic exponent z. For the S = 1/2 TAI. our dynamic scaling analysis provides η = 0.498±0.006 and z = 2.278±0.020 at T = 0, agreeing with the previous results. For the S = 3/2 TAI, after identifying a KT-transition temperature T_KT = 0.51±0.01. we find the temperature-dependent η ranging from 0.301±0.008 at T = 0.51 to 0.224±0.016 at T = 0 along the KT-line whereas the value of z = 2.20±0.06 is constant for T ≤ T_KT. It is shown that the spin S = 3/2 TAI model and the two-dimensional XY model, sharing the KT-type phase transition, exhibit similar static critical and coarsening dynamics behavior. For both the S = 1/2, 3/2 TAI. the value of z (η) is compatible with (larger than) that of the Ising model at T _c and the XY model for T ≤ T_KT in two-dimension. Our results imply that although the quasi-long-range order disappears with η_XY = 0 in the two-dimensional XY model at T = 0. the S = 3/2 TAI still maintains it with η_TAI = 0.224 due to the effect of a frustration and a high degeneracy of ground state.