  We investigate the proposal that for weakly coupled two-dimensional magnets
the transition temperature scales with a critical exponent which is equivalent
to that of the susceptibility in the underlying two-dimensional model, $ \gamma
$. Employing the exact diagonalization of transfer matrices we can determine
the critical temperature for Ising models accurately and then fit to
approximate this critical exponent. We find an additional logarithm is required
to predict the transition temperature, stemming from the fact that the heat
capacity exponent $ \alpha $ tends to zero for this Ising model, complicating
the elementary prediction. We believe that the excitations of the transfer
matrix correspond to thermalized topological excitations of the model and find
that even the simplest model exhibits significant changes of behavior for the
most relevant of these excitations as the temperature is varied.
