For a particular choice of vertex weights, the two-dimensional six-vertex model can be viewed as a probabilistic cellular automaton. Physically it describes then the surface slope of a two-dimensional solid which grows through deposition. Based on this analogy we predict the large-scale asymptotic behavior of the vertical polarization correlations. The transfer matrix commutes with a nonsymmetric spin Hamiltonian. We diagonalize it using the Bethe ansatz and prove that the dynamical scaling exponent for kinetic roughening is z=3/2 in 1+1 dimensions.

• Received 16 August 1991

DOI:https://doi.org/10.1103/PhysRevLett.68.725