MAPPING OF CRYSTAL-GROWTH ONTO THE 6-VERTEX MODEL

A simple kinetic TLK crystal model is studied, where growth and evaporation take place by attachment and detachment of atoms at kink sites along steps. Assuming the steps to run up and to the right exclusively, the model is mapped onto the 6-vertex model, where the step lines correspond to the lines obtained by marking the arrows pointing down and to the left. (Since vertex 2 is absent, the model is actually a 5-vertex model). The growth process is described by an exact master equation, which is then solved for small-size versions of the model; the growth rate is calculated in terms of the kinetic coefficients. The limit for large sizes is discussed. © 1990.