Numerical evidence of hyperscaling violation in wetting transitions of the random-bond Ising model in d=2 dimensions.

We performed extensive simulations of the random-bond Ising model confined between walls where competitive surface fields act. By properly taking the thermodynamic limit we unambiguously determined wetting transition points of the system, as extrapolation of localization-delocalization transitions of the interface between domains of different orientation driven by the respective fields. The finite-size scaling theory for wetting with short-range fields [E. V. Albano and K. Binder, Phys. Rev. Lett. 109, 036101 (2012)PRLTAO0031-900710.1103/PhysRevLett.109.036101] establishes that the average magnetization of the sample, with critical exponent β, is the proper order parameter for the study of wetting. While the hyperscaling relationship given by γ+2β=ν_{∥}+ν_{⊥} requires β=1/2 (γ=4, ν_{∥}=3, and ν_{⊥}=2), the thermodynamic scaling establishes that Δ_{s}=γ+β, which in contrast requires β=0 (Δ_{s}=4), where γ, ν_{∥}, ν_{⊥}, and Δ_{s} are the critical exponents of the susceptibility, the correlation lengths parallel and perpendicular to the interface, and the gap exponent, respectively. So, we formulate a finite-size scaling theory for wetting without hyperscaling and perform numerical simulations that provide strong evidence of hyperscaling violation (i.e., β=0) and a direct measurement of the susceptibility critical exponent γ/ν_{⊥}=2.0±0.2, in agreement with theoretical results for the strong fluctuation regime of wetting transitions with quenched noise.