Tricritical Transitions, Interface Roughening, and the ClassicalXYModel

Space renormalization group calculations are performed for a class of spin-$S$ Ising systems, using a modification of Migdal's recursion relation. Interface-roughening models are obtained when $S\to \infty$ and tricritical points and critical lines become the roughening temperature and rough phase. The latter corresponds to the low-temperature phases of the classical Coulomb gas and two-dimensional $\mathrm{XY}$ model and implications for the $\mathrm{XY}$-model exponent $\eta$ are discussed.