Effects of disorder in ferroelastics: A spin model for strain glass

We demonstrate that a strain pseudospin model for martensitic alloys predicts a glass phase in the presence of disorder, consistent with recent experiments on binary and ternary alloys that have established the existence of such a phase above a critical composition. We find that the glass phase, as characterized by the Edwards-Anderson order parameter, exists even in the absence of elastic long-range interactions, which compete with the disorder to shift the glass transition to higher values of disorder. Our model predicts a second-order phase transition between the martensite and strain glass phases as a function of the disorder. Together with the cusp in the susceptibility and the history dependence in the glass phase in zero-field-cooling and field-cooling curves, these predictions may be tested experimentally by varying the alloy composition. Our approach using mean-field analysis and Monte Carlo simulations may be generalized to the study of glassy behavior in more complex structural transformations in two and three dimensions.