Magnetic and thermal hysteresis in the O ( N )-symmetric ( Φ 2 ) 3 model

摘要: We extend our study of hysteresis to the O(N) symmetric (${\mathrm{\ensuremath{\Phi}}}^{2}$${)}^{3}$ model in three dimensions with dynamics nonconserved order parameter given by a Langevin equation. analyze both thermal and magnetic within this model. systematics shapes areas loops as functions amplitude frequency applied field other parameters theory. In case we obtain pinched for range values space demonstrate scaling behavior area loop ${\mathit{H}}_{0}$ low amplitudes: A\ensuremath{\approxeq}${\mathit{H}}_{0}^{\mathrm{\ensuremath{\alpha}}}$, where exponent \ensuremath{\alpha}=2/3. This puts same universality class that (${\mathrm{\ensuremath{\Phi}}}^{2}$${)}^{2}$ Thermal hysteresis, obtained cycling temperature presence small field, is characterized asymmetric loops. find scales function periodic (for amplitudes): A\ensuremath{\approxeq}${\mathit{r}}_{0}^{\mathrm{\ensuremath{\alpha}}}$, \ensuremath{\alpha}=1. show relevant physics ferroelectric materials charge-density-wave systems. Our observations are consistent existing experimental data on ferroelectrics charge-density waves.