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.
Amar, J., Kaski, K., & Gunton, J. D. (1984). Square-lattice-gas model with repulsive nearest- and next-nearest-neighbor interactions. Physical Review B, 29(3), 1462-1464. https://doi.org/10.1103/PhysRevB.29.1462