Cascade effects in a nonequilibrium phase transition with metallurgical relevance

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Abstract
The order-disorder transition (antiferromagnetic with conserved total spin) is studied when atomic exchanges result from two processes in parallel, as is the case under energetic particle irradiation: thermally activated jumps and ballistic jumps. The latter favor fully disordered configurations (infinite-temperature dynamics), while the former tend to restore some degree of order. The appropriate mean-field phase diagram is established. A tricritical point is identified below which the nonequilibrium order-disorder transition becomes first order. Stochastic effects are addressed by master-equation and Fokker-Planck equation techniques. Introducing ballistic jumps by bursts (replacement cascades) does not change the steady-state values of the order parameter but definitely affects their respective stability. Below the tricritical temperature, cascade effects shift the phase boundary of the first-order transition towards the spinodal ordering line.