A Model of Subdiffusive Interface Dynamics with a Local Conservation of Minimum Height

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 z2.5. 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.