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)] establishes that the average magnetization of the sample, with critical exponent beta, is the proper order parameter for the study of wetting. While the hyperscaling relationship given by gamma + 2 beta = nu(parallel to) + nu(perpendicular to) requires beta = 1 / 2 (gamma = 4, nu(parallel to) = 3, and nu(perpendicular to) = 2), the thermodynamic scaling establishes that Delta(s) = gamma + beta, which in contrast requires beta = 0 (Delta(s) = 4), where gamma, nu(parallel to), nu(perpendicular to), and Delta(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., beta = 0) and a direct measurement of the susceptibility critical exponent gamma / nu(perpendicular to) = 2.0 +/- 0.2, in agreement with theoretical results for the strong fluctuation regime of wetting transitions with quenched noise.