A RANDOM-FIELD 3-STATE SPIN MODEL TO SIMULATE HYSTERESIS AND AVALANCHES IN MARTENSITIC TRANSFORMATIONS

We propose a 3-state spin model to simulate the martensitic transition (MT) between austenite (S = 0) and two different, twin-related, marte nsitic phases (S = +/-1). The system can be driven by two fields: Delt a plays the role of temperature (drives the thermally-induced transiti on) and H plays the role of an uniaxial stress. Every spin S, in addit ion, experiences the effect of a static field h, randomly varying from site to site. The model reproduces the avalanche-like kinetics of the MT and the shape of hysteresis cycles. We obtain the phase diagram of the model, study the evolution of chi (amount of martensite) and m (t otal strain) when the system is driven by the two external fields, and discuss the return-point memory properties of the trajectories. Final ly, we study the role played by the random field on the statistical di stribution of avalanches.