  The Langevin description of systems with two symmetric absorbing states
yields a phase diagram with three different phases (disordered and active,
ordered and active, absorbing) separated by critical lines belonging to three
different universality classes (generalized voter, Ising, and directed
percolation). In this paper we present a microscopic spin model with two
symmetric absorbing states that has the property that the model parameters can
be varied in a continuous way. Our results, obtained through extensive
numerical simulations, indicate that all features of the Langevin description
are encountered for our two-dimensionsal microscopic spin model. Thus the Ising
and direction percolation lines merge into a generalized voter critical line at
a point in parameter space that is not identical to the classical voter model.
A vast range of different quantities are used to determine the universality
classes of the order-disorder and absorbing phase transitions. The
investigation of time-dependent quantities at a critical point belonging to the
generalized voter universality class reveals a more complicated picture than
previously discussed in the literature.

Statistical Mechanics