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

Abstract

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 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 Δs=γ+β, which in contrast requires β=0 (Δs=4), where γ, ν, ν, and Δs 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.