  We report on classical Monte Carlo study of phase transitions and critical
behavior of a 2D spin-pseudospin model describing a dilute magnet with
competing charge and spin interactions. The static critical exponents of the
specific heat and correlation length are calculated using the finite-size
scaling theory in a wide range of model parameters. The order of phase
transitions is analyzed within the energy histogram method. It is found that
approaching the frustration point and increasing the density of non-magnetic
impurities leads to non-universal critical behavior and first-order phase
transitions. Features of non-universal critical behavior are shown to depend on
the relationship between the parameters of the spin and pseudospin
interactions.
