Groupe de Physique Statistique

We consider first-order transitions near line defects in two-dimensional systems with a jump of the local order parameter at the continuous bulk critical point. Analyzing exact results, a general scaling theory is proposed with different analytic properties of the local thermodynamic functions below and above the bulk critical temperature. In the latter case the local temperature is a dangerous irrelevant variable, which explains the anisotropic scaling behavior and exponent asymmetry observed at this type of transition.