UNIVERSALITY CLASSES FOR LINE-DEPINNING TRANSITIONS

The universality classes and exact critical singularities for line-depinning transitions in a space of d transverse dimensions are determined using a renormalization method. Pinning potentials that fall off faster with distance than 1/r2 lead to nontrivial first-order phase transitions above the upper critical dimensionality d = 4, and to second-order transitions for d < 4. For d = 2 the free-energy density has an essential singularity of the form exp(-1/tau), were tau is the thermal scaling field. The next-nearest corrections to the free energy will be calculated for the case where the long-range part of the pinning potential decays faster than 1/r2. Pinning potentials containing an inverse square tail can give rise to a nontrivial first-order phase transition above an upper critical dimension, second-order transitions with nonuniversal exponents, or Kosterlitz-Thouless-like transitions with a multicritical point between the last two regimes, depending on the strength of the interaction. Attractive pinning potentials decaying slower than 1/r2 prevent depinning transitions at finite temperature, whereas repulsive ones in the presence of short-range attraction lead to first-order transitions.