  In this work we study the one-dimensional contact process with diffusion
using two different approaches to research the critical properties of this
model: the supercritical series expansions and finite-size exact solutions.
With special emphasis we look to the multicritical point and its crossover
exponent that characterizes the passage between DP and mean-field critical
properties. This crossover occurs in the limit of infinite diffusion rate and
our results pointed $\phi=4$ as the better estimate for the crossover exponent
in agreement with computational simulations.
