Tempered pair potential ($|v(r)|\le C{r}^{-(d+ϵ)}$)

A standard sufficient tempering condition is this tail bound beyond a fixed radius, with $ϵ>0$ in spatial dimension $d$. It makes the distant interaction tail integrable; finite-range pair potentials satisfy it. Together with a stable pair potential and suitable growing containers, such assumptions support the conventional thermodynamic limit. A Curie–Weiss model with its size-dependent coupling uses a different prescription.