Numerical simulation of the anti-ferromagnetic transition in iron-based superconductorA_2Fe_4Se_5
With Monte Carlo methods, we systematically investigate the anti-ferromagnetic transition (AFM) in the new iron-based superconductor A2Fe4Se5 (A = K;Rb;Cs; Tl) with\sqrt{5} * \sqrt{5} vacancy order, using the extended J1 - J2 model. Combing the parallel tempering technique and short-time dynamic approach, new method for the determination of the ground state, transition temperature, and static and dynamic critical exponents is developed. Taking case 1 as an example, the experimental observed block checkerboard state (BCS) is confirmed as the ground state, and a high transition temperature is identified, almost three times as large as that in case 2, corresponding to other-type iron-based superconductors. Based on the short-time dynamic scaling form, we accurately determine static and dynamic exponents for both case 1 and case 2, in comparison with those of 2D Ising model. The result indicates that case 1 belongs to 2D Ising universality class, while case 2 belongs to Suzuki's weak universality. Further analysis is performed, starting from a simpler example without n:n:n interactions, called case 3. Under the block mapping and topological transformation, an equivalence relation is revealed between the extended J1-J2 model and bathroom-tile Ising model. With this, all of the results can be understood.