SOLITARY DOMAIN WALLS AT FIRST-ORDER PHASE TRANSITIONS WITH THREE-FOLD SYMMETRY BREAKING : STATICS AND DYNAMICS

Abstract
STATICS A one-dimensional Ginzburg-Landau Lagrangian containig nonlinear contributions of a two component order parameter is considered. It may be viewd as a model describing first-order phase transitions from a high temperature parent phase into any of three variants. The structure and energy of the static ( as well as traveling) solitary boundaries connecting two different variant phases or parent-variant phases are calculated at all temperatures. Approaching the first- order transition temperature from below, the solitary boundary connecting two variants splits gradually into two parent-variant solitary domain walls of finite width. Their separation, however, diverges at the transition temperature. This temperature is the border point between two topologically different classes of domain walls, which apparently also have different nontrivial time ependence. Below the transition point the solutions are of traveling type, but above the transition temperature they have oscillatory time dependence. Linearized perturbation analysis around the stationary soliton boundaries shows them to be marginally stable below the transition temperature and unstable at the transition temperature. The structure of the lowest energy perturbation modes is also examined. DYNAMICS We present numerical results concerning solitary-antisolitary (SS) collisions for temperatures below the first-order transition point, and the sole existence of oscillatory SS arrays above the first order transition temperature. The rich spectrum of behaviors is governed by coupled nonintegrable and nonlinear wave equations which result from a model Lagrangian for a complex scalar (two-component) field ih one-space dimension, and in the presence of three fold phase anisotropy in the local potential energy density. This model reduces to the Φ⁴ model for a unique temperature. For all temperatures below the first-order transition point and for low, intermediate ; and high initial velocities, the SS collisions result in trapped states, alternating sequence of trapping and reflection, and reflection states, respectively. Only for the Φ⁴ - temperature and the first-order transition temperature the spatial characteristics of the trajectories on the order parameter plane persist both statically and dynamically. SS collisions above the Φ⁴ - temperature induce chazges in the observable physical properties of the system, whereas below this temperature the SS collisions leave the system's properties unchanged. Above the first-order transition temperature no traveling solitary wave solutions exist, but only split-solitons with oscillatory time dependence.