Anomalous tag diffusion in the asymmetric exclusion model with particles of arbitrary sizes

Anomalous behavior of correlation functions of tagged particles are studied in generalizations of the one-dimensional asymmetric exclusion problem. In these generalized models the range of the hard-core interactions are changed and the restriction of relative ordering of the particles is partially broken. The models probing these effects are those of biased diffusion of particles having size S=0,1,2, em leader, or an effective negative "size" S=-1,-2, em leader, in units of lattice space. Our numerical simulations show that irrespective of the range of the hard-core potential, as long some relative ordering of particles are kept, we find suitable sliding-tag correlation functions whose fluctuations growth with time anomalously slow (t1/3), when compared with the normal diffusive behavior (t1/2). These results indicate that the critical behavior of these stochastic models are in the Kardar-Parisi-Zhang (KPZ) universality class. Moreover a previous Bethe-ansatz calculation of the dynamical critical exponent z, for size S> or =0 particles is extended to the case S<0 and the KPZ result z=3/2 is predicted for all values of S in Z.