Exact solution of zero-temperature hysteresis in a ferromagnetic Ising chain with quenched random fields

✍ Scribed by Prabodh Shukla

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 356 KB
• Volume: 233
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/s0378-4371(96)00216-6

✦ Synopsis

A probabilistic method is used to obtain an exact solution of the zero-temperature hysteretic dynamics of a one-dimensional Ising model with quenched random fields. The result is discussed in the context of the Barkhausen noise observed in experiments as well as numerical simulations.

Growing appreciation of nonequilibrium statistical mechanics in recent years has produced a renewed effort in the study of hysteresis [1][2][3][4][5][6][7][8]. Sethna et al. [9] have proposed a microscopic model of disorder-driven hysteresis which is based on the zerotemperature single-spin-flip dynamics of an Ising model with quenched random fields. The basic mechanism of hysteresis in this model is the following. A large number of states of the system are stable fixed-points of the zero-temperature dynamics. Each fixed-point has a distinct domain of attraction which consists of the fixed-point itself, and all other states which flow into the fixed-point under the dynamics. The final state of the system under its relaxational dynamics is determined by the domain in which the system was initially present in addition to other parameters such as the amount of quenched disorder and the applied field. This builds in history-dependent effects in the system. Numerical simulations of the model produce familiar hysteresis loops. The model also offers an explanation of the noise associated with the hysteresis loops. The energy barriers between different fixed-points have a distribution of heights which depends on the details of the system. As the driving field is varied, successive barriers are crossed at different increments of the applied field giving rise to the Barkhausen noise.