English

Field Theory of Disordered Elastic Interfaces at 3-Loop Order: The $\beta$-Function

Disordered Systems and Neural Networks 2018-07-23 v2

Abstract

We calculate the effective action for disordered elastic manifolds in the ground state (equilibrium) up to 3-loop order. This yields the renormalization-group β\beta-function to third order in ϵ=4d\epsilon=4-d, in an expansion in the dimension dd around the upper critical dimension d=4d=4. The calculations are performed using exact RG, and several other techniques, which allow us to resolve consistently the problems associated with the cusp of the renormalized disorder.

Keywords

Cite

@article{arxiv.1801.08483,
  title  = {Field Theory of Disordered Elastic Interfaces at 3-Loop Order: The $\beta$-Function},
  author = {Kay Joerg Wiese and Christoph Husemann and Pierre Le Doussal},
  journal= {arXiv preprint arXiv:1801.08483},
  year   = {2018}
}

Comments

This is the first part of arXiv:1707.09802v1. The remaining part is in arXiv:1707.09802v2. 47 pages, 67 figures. v2: typos corrected and hyper-ref enabled

R2 v1 2026-06-22T23:56:29.668Z