  A semi-grand-canonical Monte Carlo algorithm is employed in conjunction with
the bond fluctuation model to investigate the critical properties of an
asymmetric binary (AB) polymer mixture. By applying the equal peak-weight
criterion to the concentration distribution, the coexistence curve separating
the A-rich and B-rich phases is identified as a function of temperature and
chemical potential. To locate the critical point of the model, the cumulant
intersection method is used. The accuracy of this approach for determining the
critical parameters of fluids is assessed. Attention is then focused on the
joint distribution function of the critical concentration and energy, which is
analysed using a mixed-field finite-size-scaling theory that takes due account
of the lack of symmetry between the coexisting phases. The essential Ising
character of the binary polymer critical point is confirmed by mapping the
critical scaling operator distributions onto independently known forms
appropriate to the 3D Ising universality class. In the process, estimates are
obtained for the field mixing parameters of the model which are compared both
with those yielded by a previous method, and with the predictions of a mean
field calculation.
