Theory of order–disorder phase transitions with over-the-barrier motion

An approximate method taking into account the over-the-barrier motion in the two-well model of structural order-disorder transition is developed. The approximation consists in a transition to the energy representation and in the replacement of exact values of dynamic variables by the values averaged over one-particle phase trajectories. The problem is reduced to a three-component model in which two states describe motion in the wells, while the third corresponds to the over-the-barrier region. The temperature and barrier height are the parameters of the effective field determining the relative population of the over-the-barrier states. The main results include the nonlinear dependence Tc(J) of the transition temperature on the pair interaction constant, the dependence of Tc on the parameters of the barrier, and a sharp increase in the share of over-the-barrier states when Tc is approached from below, which corresponds to pre-transition defreezing of the low-temperature phase dynamics.

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