A Random Field 3-State Spin Model to Simulate Hysteresis and Avalanches in Martensitic Transformations

Abstract
We propose a 3-state spin model to simulate the martensitic transition (MT) between austenite (S = 0) and two different, twin-related, martensitic phases (S=+/-1). The system can be driven by two fields : Δ plays the role of temperature (drives the thermally-induced transition) and H plays the role of an uniaxial stress. Every spin S, in addition, 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 X (amount of martensite) and m (total strain) when the system is driven by the two external fields, and discuss the return-point memory properties of the trajectories. Finally, we study the role played by the random field on the statistical distribution of avalanches.