At a critical end point a critical phase coexists with a noncritical phase \ensuremath{\alpha} and singularities arise beyond those on the associated critical line. New universal amplitude ratios are defined for the shape of the \ensuremath{\alpha}-phase boundary and for the noncritical surface tensions near end points. A postulated correspondence with wall/surface criticality leads to predictions for general dimension d that are exact at (and near) d=2 and for d\ensuremath{\ge}4 (where mean-field theory applies) and yield experimentally testable estimates for d=3.
Estimates for the critical interfacial tension amplitudes of the three-state Potts model in two dimensions via direct Monte Carlo sampling are presented for the first time. Both the square and triangular lattices are analyzed with use of finite-size scaling considerations. Also presented for the first time are estimates for the correlation-length amplitudes as derived from high-temperature series. These numerical results allow investigation of the ratio U=\ensuremath{\tau}${\ensuremath{\xi}}^{d\mathrm{\ensuremath{-}}1}$/
kBT as T\ensuremath{\rightarrow}
Tc. The results confirm the universality of U and are in agreement with exact results for hard hexagons. The finite-size scaling amplitude for the interfacial free energy at criticality is also shown to be universal within the available precision.