A radial continuum phase transition with algebraic decay

We construct a bounded, continuous, stable radial pair potential in three dimensions with $|\varphi (r)|\le C{r}^{-3-1/32}$ for r ≥ 1. Throughout an open interval of positive densities, its canonical thermodynamic free energy is finite at every positive inverse temperature and has a strict downward derivative jump at one common finite positive inverse temperature.