Year: 2023
Type: preprint
Abstract: We consider random gradient fields with disorder where the interaction potential $V_e$ on an edge $e$ can be expressed as $e^{-V_e(s)} = \int ρ(\mathrm{d}κ)\, e^{-κξ_e} e^{-\frac{κs^2}{2}}$. Here $ρ$ denotes a measure with compact support in $(0,\infty)$ and $ξ_e\in\mathbb{R}$ a nontrivial edge dependent disorder. We show that in dimension $d=2$ there is a unique shift covariant disordered gradient Gibbs measure such that the annealed measure is ergodic and has zero tilt. This shows that the phase transitions known to occur for this class of potential do not persist to the disordered setting. The proof relies on the connection of the gradient Gibbs measures to a random conductance model with compact state space, to which the well known Aizenman-Wehr argument applies.
Source: arXiv (Cornell University)
Authors: Buchholz, Simon, Cotar, Codina
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G11009315, EXC 2047: Hausdorff Center for Mathematics (HCM), G174421807, G2203179303, G3341554066, G3655418302, G3691759950, G4274133347, G457854574, Isaac Newton Institute for Mathematical Sciences, SFB 1060: Die Mathematik der emergenten Effekte, Continuous gradient interfaces with disorder, G8372877233
OpenAlex ID: W4387064191