The square-lattice gas with several ratios ($R$) of next-nearest-neighbor coupling to nearest-neighbor coupling is studied by finite-size scaling using transfer-matrix methods. Results are obtained for the phase diagram and critical exponents for the 2 × 1 and 2 × 2 order-disorder transitions, for the case $R=1\mathrm{}$. While the correlation length exponent $\nu$ seems to be nonuniversal, weak universality appears to hold for the (2 × 2) transition and possibly for the 2 × 1 transition. Reentrant behavior is observed for the 2 × 1 transition line but appears to decrease with increasing strip width. The variation of the 2 × 1 transition line with different values of $R$ ($R=1,2,5,\infty$) is also studied.

• Received 5 August 1983

DOI:https://doi.org/10.1103/PhysRevB.29.1462