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 h0c(T, f). The tricritical point in the phase diagram is also located.