Study of hysteresis phenomena in Ising-like pseudospin systems with random local reversal fields and random spin-spin interactions

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Abstract
We study the hysteresis properties of a generalization of the Sherrington–Kirkpatrick spin-glass model, including, in addition to the random spin-spin coupling costants {Jij}, a random distribution {hci} of local spin coercive fields, hindering spin flipping. The system evolution is driven by the time-dependent external field H(t). We investigate numerically the behavior as a function of H of the average magnetization per spin, m(H), and of the spin internal field distribution P(h;H). A rich variety of m(H) hysteresis loops is obtained, whose properties are controlled by the parameters of the {Jij} and {hci} distribution. It is found that the contributions of {Jij} and {hci} to the coercive field of these loops simply add to each other. An approximate Fokker–Planck equation for P(h;H) is derived, which permits one to understand the main features of P(h;H). In particular, it leads to a natural interpretation of the fact, put in evidence by computer simulations, that P(h;H) is, for small h, a linear function of h, whose slope is independent of H and of the {hci} distribution.