  The Cooperative Motion Algorithm is an efficient lattice method to simulate
dense polymer systems and is often used with two different criteria to generate
a Markov chain in the configuration space. While the first method is the
well-established Metropolis algorithm, the other one is an heuristic algorithm
which needs justification. As an introductory step towards justification for
the 3D lattice polymers, we study a simple system which is the binary equimolar
uid on a 2D triangular lattice. Since all lattice sites are occupied only
selected type of motions are considered, such the vacancy movements, swapping
neighboring lattice sites (Kawasaki dynamics) and cooperative loops. We compare
both methods, calculating the energy as well as heat capacity as a function of
temperature. The critical temperature, which was determined using the Binder
cumulant, was the same for all methods with the simulation accuracy and in
agreement with the exact critical temperature for the Ising model on the 2D
triangular lattice. In order to achieve reliable results at low temperatures we
employ the parallel tempering algorithm which enables simultaneous simulations
of replicas of the system in a wide range of temperatures.
