  Monte Carlo simulations are used to study lattice gases of particles with
extended hard cores on a two dimensional square lattice. Exclusions of one and
up to five nearest neighbors (NN) are considered. These can be mapped onto hard
squares of varying side length, $\lambda$ (in lattice units), tilted by some
angle with respect to the original lattice. In agreement with earlier studies,
the 1NN exclusion undergoes a continuous order-disorder transition in the Ising
universality class. Surprisingly, we find that the lattice gas with exclusions
of up to second nearest neighbors (2NN) also undergoes a continuous phase
transition in the Ising universality class, while the Landau-Lifshitz theory
predicts that this transition should be in the universality class of the XY
model with cubic anisotropy. The lattice gas of 3NN exclusions is found to
undergo a discontinuous order-disorder transition, in agreement with the
earlier transfer matrix calculations and the Landau-Lifshitz theory. On the
other hand, the gas of 4NN exclusions once again exhibits a continuous phase
transition in the Ising universality class -- contradicting the predictions of
the Landau-Lifshitz theory. Finally, the lattice gas of 5NN exclusions is found
to undergo a discontinuous phase transition.
