Dynamic phase transition in the Heisenberg model under a time-dependent oscillating field

We derive a new three-dimensional mean-field equation of motion for the average magnetization with a Heisenberg model, and calculate the time averaged magnetization components Qz and Qx, and the average hysteresis-loop area components Az and Ax. A dynamic H0-T transition phase diagrams from Q≠0 to Q=0 for the 2D and 3D cases are obtained. It is found that the dynamic behavior for the Heisenberg model is different from that for the Ising model. The phase diagrams with different coordinate number z and the orientation number of spin n have been well explained using the competition between the relaxation time and the period of the external magnetic field. A dynamical scaling, A∼H0aϖbξ[ϖH0γ], is studied, and the best exponents a,b and γ with the best data collapse are obtained. For the 3D case, two different scaling expressions are valid in the low and high frequency regions, respectively. For the 2D case, however, one scaling relationship is suitable for the whole frequency region.