Typical and Exceptional Shape Fluctuations of Interacting Strings

1-dimensional strings governed by a finite tension are studied in d = 1 + d ⊥ dimensions. In the presence of a short-ranged attractive interaction, two strings undergo a nontrivial unbinding transition for any value of d ⊥ . The characteristic unbinding temperature T * vanishes as 1/ d ⊥ for large d ⊥ . The critical exponents evolve with d ⊥ in a singular and nonmonotonic way. For d ⊥ < 4, the typical string fluctuations consist of humps with roughness exponent ζ = 1/2; for d ⊥ > 4, on the other hand, these humps become more and more exceptional as the transition is approached and are then governed by a power law distribution.