Solution of lattice gas models in the generalized ensemble on the Bethe lattice

We present the exact Bethe lattice solution for a lattice gas Potts model d efined in the generalized ensemble which was previously studied in elucidat ing the anomalous thermodynamic properties of water. For this model the loc us of density maxima (TMD), the locus of isothermal compressibility extrema , (TEC), the spinodal curve, and the percolation curve; for four hydrogen b onded molecules are calculated using the Bethe lattice solution. The result s confirm qualitative relationships between the TMD, the TEC, and the perco lation curve obtained previously from a mean field calculation, [S1063-651X (99)17205-2].