Square-lattice-gas model with repulsive nearest- and next-nearest-neighbor interactions

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 $R=1$. While the correlation length exponent ν 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,∞) is also studied.