  The principle and the efficiency of the Monte Carlo transfer-matrix algorithm
are discussed. Enhancements of this algorithm are illustrated by applications
to several phase transitions in lattice spin models. We demonstrate how the
statistical noise can be reduced considerably by a similarity transformation of
the transfer matrix using a variational estimate of its leading eigenvector, in
analogy with a common practice in various quantum Monte Carlo techniques. Here
we take the two-dimensional coupled $XY$-Ising model as an example.
Furthermore, we calculate interface free energies of finite three-dimensional
O($n$) models, for the three cases $n=1$, 2 and 3. Application of finite-size
scaling to the numerical results yields estimates of the critical points of
these three models. The statistical precision of the estimates is satisfactory
for the modest amount of computer time spent.
