The theory of interface localization in near-critical planar systems at phase coexistence is formulated from first principles. We show that mutual delocalization of two interfaces, amounting to interfacial wetting, occurs when the bulk correlation length critical exponent ν is larger than or equal to 1. Interaction with a boundary or defect line involves an additional scale and a dependence of the localization strength on the distance from criticality. The implications are particularly rich in the boundary case, where delocalization proceeds through different renormalization patterns sharing the feature that the boundary field becomes irrelevant in the delocalized regime. The boundary delocalization (wetting) transition is shown to be continuous, with surface specific heat and layer thickness exponents which can take values that we determine.
The theory of interface localization in near-critical planar systems at phase coexistence is formulated from first principles. We show that mutual delocalization of two interfaces, amounting to interfacial wetting, occurs when the bulk correlation length critical exponent ν is larger than or equal to 1. Interaction with a boundary or defect line involves an additional scale and a dependence of the localization strength on the distance from criticality. The implications are particularly rich in the boundary case, where delocalization proceeds through different renormalization patterns sharing the feature that the boundary field becomes irrelevant in the delocalized regime. The boundary delocalization (wetting) transition is shown to be continuous, with surface specific heat and layer thickness exponents which can take values that we determine.
We consider two-dimensional (d = 2) systems with short-ranged microscopic interactions, where interface unbinding (wetting) transitions occur in the limit of vanishing temperature T .For T = 0 the transition is characterized by non-universal critical properties analogous to those established for thermal wetting transitions in d = 3, albeit with a redefined capillary parameter ω.Within a functional renormalization-group treatment of an effective interfacial model, we compute the finite-temperature phase diagram, exhibiting a line of interface unbinding transitions, terminating at T = 0 with an interfacial quantum-critical point.We identify distinct scaling regimes, reflecting the interplay between quantum and thermal interfacial fluctuations.A crossover line marking the onset of the quantum-critical regime is described by the d = 3 interfacial correlationlength exponent ν || .This potentially opens another way to investigate the non-universal character of ν || .On the other hand, the emergent interfacial quantum-critical regime shows no signatures of non-universality.
We consider interfacial phenomena accompanying bulk quantum phase transitions in the presence of surface fields. On general grounds we argue that the surface contribution to the system free energy involves a line of singularities characteristic of an interfacial phase transition, occurring below the bulk transition temperature Tc down to T=0. This implies the occurrence of an interfacial quantum critical regime extending into finite temperatures and located within the portion of the phase diagram where the bulk is ordered. Even in situations where the bulk order sets in discontinuously at T=0, the system's behavior at the boundary may be controlled by a divergent length scale if the tricritical temperature is sufficiently low. Relying on an effective interfacial model we compute the surface phase diagram in bulk spatial dimensionality $d\ensuremath{\geqslant}2$ and extract the values of the exponents describing the interfacial singularities in $d\ensuremath{\geqslant}3$.
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 $\ensuremath{\beta}$, is the proper order parameter for the study of wetting. While the hyperscaling relationship given by $\ensuremath{\gamma}+2\ensuremath{\beta}={\ensuremath{\nu}}_{\ensuremath{\parallel}}+{\ensuremath{\nu}}_{\ensuremath{\perp}}$ requires $\ensuremath{\beta}=1/2$ ($\ensuremath{\gamma}=4, {\ensuremath{\nu}}_{\ensuremath{\parallel}}=3$, and ${\ensuremath{\nu}}_{\ensuremath{\perp}}=2$), the thermodynamic scaling establishes that ${\mathrm{\ensuremath{\Delta}}}_{s}=\ensuremath{\gamma}+\ensuremath{\beta}$, which in contrast requires $\ensuremath{\beta}=0$ (${\mathrm{\ensuremath{\Delta}}}_{s}=4$), where $\ensuremath{\gamma}, {\ensuremath{\nu}}_{\ensuremath{\parallel}}, {\ensuremath{\nu}}_{\ensuremath{\perp}}$, and ${\mathrm{\ensuremath{\Delta}}}_{s}$ 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., $\ensuremath{\beta}=0$) and a direct measurement of the susceptibility critical exponent $\ensuremath{\gamma}/{\ensuremath{\nu}}_{\ensuremath{\perp}}=2.0\ifmmode\pm\else\textpm\fi{}0.2$, in agreement with theoretical results for the strong fluctuation regime of wetting transitions with quenched noise.
Using the quasiexact density-matrix renormalization-group method and ground-state analysis we study interface delocalization transitions in wide two-dimensional Ising strips subject to long-ranged boundary fields with opposite signs at the two surfaces. Based on this approach, our explicit calculations demonstrate that critical wetting transitions do exist for semi-infinite two-dimensional systems even if the corresponding effective interface potentials decay asymptotically for large l as slow as l(-delta) with delta<2, where l is the distance of the mean interface position from the one-dimensional surface. This supersedes opposite claims by Kroll and Lipowsky [Phys. Rev. B 28, 5273 (1983)] and by Privman and Svrakić [Phys. Rev. B 37, 5974 (1988)] obtained within effective interface models. The corresponding wetting phase diagram is determined, including the cases delta=2 and delta=49 with the latter mimicking short-ranged surface fields. Our analysis highlights the limits of reliability of effective interface models.
We examine critical adsorption for semi-infinite thermodynamic systems of the Ising universality class when they are in contact with a wall of the so-called normal surface universality class in spatial dimension d=3 and in the mean-field limit. We apply local-functional theory and Monte Carlo simulations in order to quantitatively determine the properties of the energy density as the primary scaling density characterizing the critical behaviors of Ising systems besides the order parameter. Our results apply to the critical isochore, near two-phase coexistence, and along the critical isotherm if the surface and the weak bulk magnetic fields are either collinear or anticollinear. In the latter case, we also consider the order parameter, which so far has yet to be examined along these lines. We find the interface between the surface and the bulk phases at macroscopic distances from the surface, i.e., the surface is "wet." It turns out that in this case the usual property of monotonicity of primary scaling densities with respect to the temperature or magnetic field scaling variable does not hold for the energy density due to the presence of this interface.
A long-standing problem in condensed matter physics concerns the nature of the critical wetting phase transition in the Ising model or, more generally, in 3D systems with short-ranged forces.This is of fundamental interest because 3D corresponds to the upper critical dimension of the transition and it is not clear a priori whether the behaviour of the system will be mean-field-like or fluctuation-dominated.Renormalization group studies of the standard coarse-grained effective interfacial Hamiltonian model famously predict strong non-universal critical exponents which depend on the value of the so-called wetting parameter ω.However, these predictions are at odds with extensive Monte Carlo simulations of wetting in the Ising model, due to Binder, Landau and coworkers, which appear to be more mean-field-like.Further amendments to the interfacial Hamiltonian, which included the presence of a position-dependent stiffness, worsened the problem by paradoxically predicting fluctuation-induced first-order wetting behaviour.Here we show from re-analysis of a microscopic Landau-Ginzburg-Wilson model of 3D short-ranged wetting that correlation functions are characterized by two diverging parallel length scales, not one, as previously thought.This has a simple diagrammatic explanation using a non-local interfacial Hamiltonian and yields a thermodynamically consistent theory of wetting in keeping with exact sum rules.The non-local model crucially contains long-ranged two-body interfacial interactions, characterized by the new length scale, which were missing in earlier treatments.For critical wetting the second length cuts off the spectrum of interfacial fluctuations determining the repulsion from the wall.We show how this corrects previous renormalization group predictions for fluctuation effects, based on local interfacial Hamiltonians.In particular, lowering the cut-off leads to a substantial reduction in the effective value of the wetting parameter controlling the non-universality and also prevents the transition being driven first-order.Quantitative comparison with the Ising model simulation studies is also made.