Ageing in the critical contact process: a Monte Carlo study

José J. Ramasco1, Malte Henkel2, Maria Augusta Santos1 and Constantino A. da Silva Santos1
1Centro de Física do Porto and Departamento de Física, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal.
2Laboratoire de Physique des Matériaux, Université Henri Poincaré Nancy I, B.P. 239, F-54506 Vandœuvre-lès-Nancy Cedex, France.

(June 2004)

The long-time dynamics of the critical contact process which is brought suddenly out of an uncorrelated initial state undergoes ageing in close analogy with quenched magnetic systems. In particular, we show through Monte Carlo simulations in one and two dimensions and through mean-field theory that time-translation invariance is broken and that dynamical scaling holds. We find that the autocorrelation and autoresponse exponents lambda_Gamma and lambda_R are equal but, in contrast to systems relaxing to equilibrium, the ageing exponents a and b are distinct. A recent proposal to define a non-equilibrium temperature through the short-time limit of the fluctuation-dissipation ratio is therefore not applicable.