We present a finite-size-scaling study of a two-dimensional square-lattice-gas model with nearest-neighbor repulsion and next-nearest-neighbor attraction. This system may be used as a simplified model of adsorbates on transition-metal (100) surfaces. An accurate determination of the tricritical temperature is obtained by the utilization of the degeneracy of the three largest eigenvalues of the transfer matrix at a tricritical point. We obtain the phase diagram and critical and tricritical exponents, all quite consistent with previously known results. We also find that a recent conjecture relating the critical exponent η to the correlation-length amplitude seems to work well even at the tricritical point.
Rikvold, P. A., Kinzel, W., Gunton, J. D., & Kaski, K. (1983). Finite-size-scaling study of a two-dimensional lattice-gas model with a tricritical point. Physical Review B, 28(5), 2686-2692. https://doi.org/10.1103/PhysRevB.28.2686