The dynamics of a driven harmonic oscillator coupled to pairwise interacting Ising spins in random fields

Abstract

In general we are interested in dynamical systems coupled to complex hysteresis. Therefore as a first step we investigated recently the dynamics of a periodically driven damped harmonic oscillator coupled to independent Ising spins in a random field. Although such a system does not produce hysteresis, we showed how to characterize the dynamics of such a piecewise-smooth system, especially in the case of a large number of spins [P. Zech, A. Otto, and G. Radons, Phys. Rev. E 101, 042217 (2020)]. In this paper we extend our model to spin dimers, thus pairwise interacting spins. We show in which cases two interacting spins can show elementary hysteresis and we give a connection to the Preisach model, which allows us to consider an infinite number of spin-pairs. This thermodynamic limit leads us to a dynamical system with an additional hysteretic force in the form of a generalized play operator. By using methods from general chaos theory, piecewise-smooth system theory and statistics we investigate the chaotic behavior of the dynamical system for a few spins and also in case of a larger number of spins by calculating bifurcation diagrams, Lyapunov exponents, fractal dimensions and self-averaging properties. We find that the fractal dimensions and the magnetization are in general not self-averaging quantities. We show, how the dynamical properties of the piecewise-smooth system for a large number of spins differs from the system in its thermodynamic limit.

References in corpus (17)

• Dynamics of Viscoplastic Deformation in Amorphous Solids
• Crackling Noise
• Hysteresis and hierarchies: dynamics of disorder-driven first-order phase transformations
• Avalanches, Barkhausen Noise, and Plain Old Criticality
• Hysteresis, Avalanches, and Disorder Induced Critical Scaling: A Renormalization Group Approach
• Quantum Spin Dimers from Chiral Dissipation in Cold-Atom Chains
• Manipulation of Dzyaloshinskii-Moriya interaction in Co/Pt multilayers with strain
• Hysteresis in the Random Field Ising Model and Bootstrap Percolation
• A generic $C^1$ map has no absolutely continuous invariant probability measure
• Exact Solution of Return Hysteresis Loops in One Dimensional Random Field Ising Model at Zero Temperature
• Reduction of magnetostatic interactions in self-organized arrays of nickel nanowires using atomic layer deposition
• Return to return point memory
• A nano-carbon route to rare earth free permanent magnetism
• Hysteresis and avalanches in the T=0 random-field Ising model with 2-spin-flip dynamics
• Hysteresis in the T=0 RFIM: beyond metastable dynamics
• Preisach models of hysteresis driven by Markovian input processes
• The dynamics of a driven harmonic oscillator coupled to independent Ising spins in random fields