We extended the Broad Histogram Method in order to obtain spectral degenera
cies for systems with multiparametric Hamiltonians. As examples, we obtaine
d the critical lines for the square lattice Ising model with nearest- and n
ext-nearest-neighbor interactions and the antiferromagnetic Ising model in
an external field. For each system, the entire critical line is obtained us
ing data from a single computer run. We also discuss the accuracy and effic
iency of our method. (C) 2000 Elsevier Science Ltd. All rights reserved.