Temperature-induced crossovers in the static roughness of a one-dimensional interface

Abstract

At finite temperature and in presence of disorder, a one-dimensional elastic interface displays different scaling regimes at small and large lengthscales. Using a replica approach and a Gaussian variational method ͑GVM͒, we explore the consequences of a finite interface width on the small-lengthscale fluctuations. We compute analytically the static roughness B͑r͒ of the interface as a function of the distance r between two points on the interface. We focus on the case of short-range elasticity and random-bond disorder. We show that for a finite width two temperature regimes exist. At low temperature, the expected thermal and randommanifold regimes, respectively, for small and large scales, connect via an intermediate "modified" Larkin regime, that we determine. This regime ends at a temperature-independent characteristic "Larkin" length. Above a certain characteristic temperature that we identify, this intermediate regime disappears. The thermal and random-manifold regimes connect at a single crossover lengthscale, that we compute. This is also the expected behavior for zero width. Using a directed polymer description, we also study via a second GVM procedure and generic scaling arguments, a modified toy model that provides further insights on this crossover. We discuss the relevance of the two GVM procedures for the roughness at large lengthscale in those regimes. In particular, we analyze the scaling of the temperature-dependent prefactor in the roughness B͑r͒ϳT 2þ r 2 and its corresponding thorn exponent þ. We briefly discuss the consequences of those results for the quasistatic creep law of a driven interface, in connection with previous experimental and numerical studies.

Kardar-Parisi-Zhang equation with short-range correlated noise: Emergent symmetries and nonuniversal observables

“…In particular, the induced modification of the flow equation ofĝ k cannot be computed within NLO approximation, such that the RG flow of the theory is constrained to preserve the identity exponent χ + z = 2 at the IR fixed point. However, the presence of temporal correlations do not affect the results found in [62,63,65,66] (where the full time evolution is considered) in any noticeable way when compared to results obtained in a Galilean invariant set-up. This strongly suggests that the IR physics is indeed Galilean invariant.…”

“…The role of a finite ξ has been addressed in a series of previous studies in the language of the 1+1 DP endpoint [62][63][64][65][66][67] and recently in [68,69], combining analytical and numerical approaches to characterise the complete time dependence of the KPZ fluctuations, starting from the socalled 'sharp-wedge' initial condition. It was predicted in particular (within the Gaussian Variational Method (GVM) and a Bethe ansatz analysis as well as with a direct numerical integration of the correlated KPZ equation) that the amplitude of the KPZ fluctuations must display a crossover, as ξ is tuned, from the exact solution of the uncorrelated case (ξ = 0) [4,5,33] to a regime of large-scale correlations.…”

Finite-temperature crossovers in periodic disordered systems

“…Note that although this length scale is always present in our purely elastic model, it is even more subject to the constraints on the high-temperature limit (in a model where melting, i.e., the presence of topological defects can occur) than the two other length scales. Indeed, (15) can be written for small as…”

“…In particular, for interfaces this question has recently been the focus of several studies (see, e.g., Refs. [14][15][16][17] and references therein).…”

Distribution of the time at whichNvicious walkers reach their maximal height

“…A recent discussion of the toy model and its applications to the DPRM can be found in Ref. [70]. We also mention that physical observables related to X M have been studied for the DPRM in different geometry, such as the winding number of the optimal polymer on a cylinder [71].…”