Critical hysteresis in random-field XY and Heisenberg models

Hysteresis and return point memory in the random-field Blume-Capel model

We study the zero-temperature steady-state of the random-field Blume-Capel model with spin-flip Glauber dynamics on a random regular graph. The magnetization m as a function of the external field H is observed to have double hysteresis loops with a return point memory. We also solve the model on a Bethe lattice in the approximation that the spin relaxation dynamics is abelian and find good agreement between simulations on random regular graphs and Bethe lattice calculations for negative values of H.

Period multiplication cascade at the order-by-disorder transition in uniaxial random field XY magnets

Uniaxial random field disorder induces a spontaneous transverse magnetization in the XY model. Adding a rotating driving field, we find a critical point attached to the number of driving cycles needed to complete a limit cycle, the first discovery of this phenomenon in a magnetic system. Near the critical drive, time crystal behavior emerges, in which the period of the limit cycles becomes an integer n > 1 multiple of the driving period. The period n can be engineered via specific disorder patterns. Because n generically increases with system size, the resulting period multiplication cascade is reminiscent of that occurring in amorphous solids subject to oscillatory shear near the onset of plastic deformation, and of the period bifurcation cascade near the onset of chaos in nonlinear systems, suggesting it is part of a larger class of phenomena in transitions of dynamical systems. Applications include magnets, electron nematics, and quantum gases.

Analysis of wasp-waisted hysteresis loops in magnetic rocks

The random-field Ising model of hysteresis is generalized to dilute magnets and is solved on a Bethe lattice. Exact expressions for the major and minor hysteresis loops are obtained. In the strongly dilute limit the model provides a simple and useful understanding of the shapes of hysteresis loops in magnetic rock samples.

Hysteresis in the antiferromagnetic random-field Ising model at zero temperature

We study hysteresis in antiferromagnetic random-field Ising model at zero temperature. The external field is cycled adiabatically between -∞ and ∞. Two different distributions of the random field are considered: (i) a uniform distribution of width 2Δ centered at the origin and (ii) a Gaussian distribution with average value zero and standard deviation σ. In each case the hysteresis loop is determined exactly in one dimension and compared with numerical simulations of the model.