A model of subdiffusive interface dynamics with a local conservation of minimum height

Abstract

We define a new model of interface roughening in one dimension which has the property that the minimum of interface height is conserved locally during the evolution. This model corresponds to the limit q → ∞ of the q-color dimer deposition-evaporation model introduced by us earlier [Hari Menon and Dhar, J. Phys. A: Math. Gen. 28:6517 (1995)]. We present numerical evidence from Monte Carlo simulations and the exact diagonalization of the evolution operator on finite rings that growth of correlations in this model is subdiffusive with dynamical exponent z ≈ 2.5. For periodic boundary conditions, the variation of the gap in the relaxation spectrum with system size appears to involve a logarithmic correction term. Some generalizations of the model are briefly discussed.