Interplay between Ising and six-vertex symmetries in a model for the roughening of reconstructing surfaces

Abstract

The authors study a generalization of the solid-on-solid (SOS) model recently proposed for the roughening transition of reconstructing and non-reconstructing FCC (110) solid surfaces. The generalized model is expressed in terms of Ising variables representing nearest-neighbour atomic column height differences. The model is solved exactly for the order-disorder transition, obtained in the limit where all possible Ising configurations are allowed. In the opposite limit, where the local height conservation rule is imposed to recover the BCSOS (or six-vertex) symmetry, finite-size transfer-matrix calculations yield a phase diagram where the reconstruction transition (corresponding to the order-disorder transition in the other limit) is smeared out, and a roughening transition occurs at a higher temperature. The phase boundaries obtained in the two limits (Ising and BCSOS) are compared. The model Hamiltonian contains a single parameter ( lambda ), which connects in a natural way these limiting cases ( lambda =0 and respectively). The authors study by finite-size calculations a simplified version of this Hamiltonian, named the lambda -model, which just interpolates between the simple Ising model and Rys's F-model. In particular, they analyse the behaviour of the correlation length and the heat capacity peak for the whole range of values of lambda , and the step energy for lambda large enough.