  We investigate a model of self-avoiding walk exhibiting a first-order
coil-globule transition. This first-order nature, unravelled through the
coexistence of distinct coil and globule populations, has observable
consequences on the scaling properties. A thorough analysis of the size
dependence of the mean radius of gyration evidences a breakdown of the plain
tricritical scaling behaviour. In some regimes, anomalous exponents are
observed in the transition region and logarithmic corrections arise along the
coexistence curve.
