Dynamical scaling analysis of symmetry breaking for the antiferromagnetic triangular Heisenberg model in a uniform magnetic field

Phase transitions for the two-dimensional antiferromagnetic triangular Heisenberg model in a uniform field are primarily analyzed using dynamical scaling analysis. The system has ${Z}₃$ and $O(2)$ symmetries. The transition temperatures and types of transition are investigated using the relaxation of order parameters and the asymptotic behaviors of relaxation time around transition temperatures. In the low-field range, the order parameters for the ${Z}₃$ and $O(2)$ symmetries exhibit the behavior typical of a second-order transition and Kosterlitz-Thouless (KT) transition, respectively, with distinct transition temperatures. In the high-field range, an order parameter for the ${Z}₃$ symmetry exhibits the behavior of a second-order transition, while another order parameter related to the components perpendicular to the field demonstrates that the relaxation time diverges with an asymptotic form, indicating a second-order transition rather than a KT transition. These transition temperatures are estimated to be close. Critical exponents for these two order parameters are estimated separately by calculating the relaxation of fluctuations in the high-field range. It was confirmed that the critical exponents for both of these order parameters change continuously as a function of field, and they are distinct from each other.