Phase-transition behavior of a hard-core lattice gas with a tricritical point

The phase-transition behavior of a hard-core lattice gas with nearest-neighbor exclusion and next-nearest-neighbor attraction on the plane-square lattice has been determined using high- and low-density activity series including double series in the sublattice activities reported here. The model exhibits a line of second-order transition points at high temperature and a line of first-order transition points at low temperature intersecting at a tricritical point. The series for the various thermodynamic functions do not converge equally well at all temperatures, requiring the utilization of a strict criterion (outlined here) for assessing the reliability of numerical results. From the combined behavior of the thermodynamic functions we have determined the radius of convergence of the series at all temperatures, the position of the singularities (in terms of the fugacity) on the real axis approaching the intersection of the unit circle at low temperature. Along the second-order line the critical exponents are estimated to be $\alpha \simeq 0.0$ (logarithmic singularity), $\beta \simeq \frac{1}{8}$, and $\gamma \simeq \frac{7}{4}$. At the tricritical point ${\alpha }_t\simeq 1$ and ${\gamma }_t\simeq 1$ are in agreement with the $\epsilon$-expansion results of Stephens and McCauley for $d=2\mathrm{}$. The density series are poorly behaved, and we can only estimate the phase diagram.