Husimi-lattice solutions and the coherent-anomaly-method analysis for hard-square lattice gases

Although lattice gases composed of particles preventing up to their $k\mathrm{th}$ nearest neighbors from being occupied (the $k\mathrm{NN}$ models) have been widely investigated in the literature, location and universality class fluid-columnar transition 2NN model on square are still a topic debate. Here, we present grand-canonical solutions this Husimi lattices built with diagonal lattices, $2L(L+1)$ sites, for $L\ensuremath{\leqslant}7$. The systematic sequence mean-field confirms existence continuous system, extrapolations critical chemical potential ${\ensuremath{\mu}}_{2,c}(L)$ particle density ${\ensuremath{\rho}}_{2,c}(L)$ $L\ensuremath{\rightarrow}\ensuremath{\infty}$ yield estimates these quantities close agreement previous results lattice. To confirm reliability approach, employ it also 1NN model, where very accurate parameters ${\ensuremath{\mu}}_{1,c}$ ${\ensuremath{\rho}}_{1,c}$---for fluid-solid lattice---are found data $L\ensuremath{\leqslant}6$. nonclassical exponents transitions through coherent anomaly method (CAM), which case yields $\ensuremath{\beta}$ $\ensuremath{\nu}$ differing by at most 6% expected Ising exponents. For CAM analysis is somewhat inconclusive, because sensibly depend value ${\ensuremath{\mu}}_{2,c}$ used calculate them. Notwithstanding, our suggest that considerably larger than Ashkin-Teller reported numerical studies system.