Six-vertex model, roughened surfaces, and an asymmetric spin Hamiltonian.

an Asymmetric Spin Hamiltonian Leh-Hun Gwa Department of Mathematics, Rutgers University New Brunswick, NJ 08903, USA Herbert Spohn Theoretische Physik, Universit at M unchen Theresienstr. 37, D-8000 M unchen 2, Germany Abstract 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 asymptotics 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.