Monte Carlo study of hysteretic response and relaxation in Ising models

We have studied, using Monte Carlo (MC) simulations for ferromagnetic Ising systems in two to four dimensions, the variations of “hysteretic” loop area A with frequency f and amplitude h0 of the applied external magnetic field and temperature T of the system. The variations in A are fitted to a scaling form, assumed to be valid over a wide range of parameter (f, h0, T) values and the best fit exponents are obtained in all three dimensions (d = 2, 3, 4). We also compared the scaling behaviour for A, obtained from the mean field (MF) solution of the Ising dynamics. Our observations, both from the MC simulations (in d = 2 to 4) and from the MF solutions, indicate nonvanishing paramagnetic loop area A. We confirmed these MC observations by checking the finite size variation and also studied the same for a one-dimensional chain for comparison. We additionally studied the dynamic phase transition for the time averaged magnetisation (over a cycle), which acquires a nonzero value below a critical field amplitude hc0(T, f). The tricritical point in the phase diagram is also located.