Energy landscapes, lowest gaps, and susceptibility of elastic manifolds at zero temperature

Abstract

We study the effect of an external field on (1+1) and (2+1) dimensional elastic manifolds, at zero temperature and with random bond disorder. Due to the glassy energy landscape the configuration of a manifold changes often in abrupt, ``first order'' -type of large jumps when the field is applied. First the scaling behavior of the energy gap between the global energy minimum and the next lowest minimum of the manifold is considered, by employing exact ground state calculations and an extreme statistics argument. The scaling has a logarithmic prefactor originating from the number of the minima in the landscape, and reads $ΔE_1 \sim L^θ[\ln(L_z L^{-ζ})]^{-1/2}$, where $ζ$ is the roughness exponent and $θ$ is the energy fluctuation exponent of the manifold, $L$ is the linear size of the manifold, and $L_z$ is the system height. The gap scaling is extended to the case of a finite external field and yields for the susceptibility of the manifolds $χ_{tot} \sim L^{2D+1-θ} [(1-ζ)\ln(L)]^{1/2}$. We also present a mean field argument for the finite size scaling of the first jump field, $h_1 \sim L^{d-θ}$. The implications to wetting in random systems, to finite-temperature behavior and the relation to Kardar-Parisi-Zhang non-equilibrium surface growth are discussed.