  The universal critical point ratio $Q$ is exploited to determine positions of
the critical Ising transition lines on the phase diagram of the Ashkin-Teller
(AT) model on the square lattice. A leading-order expansion of the ratio $Q$ in
the presence of a non-vanishing thermal field is found from finite-size scaling
and the corresponding expression is fitted to the accurate perturbative
transfer-matrix data calculations for the $L\times L$ square clusters with
$L\leq 9$.
