Finite temperature Functional RG, droplets and decaying Burgers Turbulence

TL;DR

This paper reexamines the finite temperature functional renormalization group approach to pinning phenomena, providing exact solutions and connections to Burgers turbulence and droplet probabilities across dimensions.

Contribution

It offers a high-order beta function analysis, resolves ambiguities at zero temperature, and establishes exact solutions relating FRG, droplets, and Burgers turbulence.

Findings

Exact T=0 fixed point for the Sinai model

Thermal boundary layer form of R(u) at T>0

Connection between FRG and decaying Burgers turbulence

Abstract

The functional RG (FRG) approach to pinning of $d$-dimensional manifolds is reexamined at any temperature $T$. A simple relation between the coupling function $R(u)$ and a physical observable is shown in any $d$. In $d=0$ its beta function is displayed to a high order, ambiguities resolved; for random field disorder (Sinai model) we obtain exactly the T=0 fixed point $R(u)$ as well as its thermal boundary layer (TBL) form (i.e. for $u \sim T$) at $T>0$. Connection between FRG in $d=0$ and decaying Burgers is discussed. An exact solution to the functional RG hierarchy in the TBL is obtained for any $d$ and related to droplet probabilities.