Janus van der waals equations for real molecules with two-sided phase transitions - Kim, Jihwan; Kim, Do-Hyun; Park, Jeong-Hyuck (Frontiers in Physics, 2022)
We obtain families of generalised van der Waals equations characterised by an even number (n=2,4,6) and a continuous free parameter which is tunable for a critical compressibility factor. Each equation features two adjacent critical points which have a common critical temperature Tc and arbitrarily close two critical densities. The critical phase transitions are naturally two-sided: the critical exponents are α_P=γ_P=2/3, β_P=δ^-1=1/3 for T>Tc and α_P=γ_P=n/(n+1), β_P=δ^-1=1/(n+1) for T