Transfer matrix for the restricted canonical and microcanonical ensembles

The numerical transfer matrix for the partition function of discrete lattice models is generalized to allow the calculation of the density of states Omega(E), and the restricted density of states Omega(E,M). Given Omega(E,M) the partition function is expressed as a polynomial in the variables x=e(beta h) and y=e(-beta). These algorithms are illustrated with calculations for the Ising model on finite square lattices. The zeros of the partition function are examined in both the complex x and y planes. Finite size scaling analysis of the zeros leads to very accurate estimates for the critical temperature and critical exponents.