Approach to the lower critical dimension of the φ4 theory in the derivative expansion of the functional renormalization group

Scientific paper - Original scientific paper

• Author: Lucija Nora Farkaš
• Author: Gilles Tarjus
• Author: Ivan Balog
• Author's institution: University of Zagreb; Faculty of Science; (Department of Physics)
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics

Abstract (english)

We revisit the approach to the lower critical dimension 𝑑lc in the Ising-like 𝜑4 theory within the functional renormalization group by studying the lowest approximation levels in the derivative expansion of the effective average action. Our goal is to assess how the latter, which provides a generic approximation scheme valid across dimensions and found to be accurate in 𝑑≥2, is able to capture the long-distance physics associated with the expected proliferation of localized excitations near 𝑑lc. We show that the convergence of the fixed-point effective potential is nonuniform in the field when 𝑑→𝑑lc with the emergence of a boundary layer around the minimum of the potential. This allows us to make analytical predictions for the value of the lower critical dimension 𝑑lc and for the behavior of the critical temperature as 𝑑→𝑑lc, which are both found in fair agreement with the known results. This confirms the versatility of the theoretical approach.

• Keywords (english): lower critical dimension 𝑑lc; functional renormalization group
• Language: english
• Publication type: Scientific paper - Original scientific paper
• Publication status: Published
• Peer review: Peer review - international
• Publication version: Published version
• Journal title: Physical Review E
• Numbering: vol. 108, no. 5, 054107
• p-ISSN: 2470-0045
• e-ISSN: 2470-0053
• DOI: https://doi.org/10.1103/PhysRevE.108.054107
• URN:NBN: urn:nbn:hr:217:984051
• Publication: 2023-11
• Project: Number: KK.01.1.1.01.0004; Title (croatian): Provedba vrhunskih istraživanja u sklopu Znanstvenog centra izvrsnosti za kvantne i kompleksne sustave te reprezentacije Liejevih algebri; Title (english): Implementation of top research within the Scientific Center of Excellence for Quantum and Complex Systems, and Representations of Lie Algebras; Acronym: QuantiXLie; Leader: Hrvoje Buljan; Jurisdiction: eu; Funding stream: European Regional Development Fund
• Document URL: https://link.aps.org/doi/10.1103/PhysRevE.108.054107
• Type of resource: Text
• Access conditions: Open access
• Public note: © 2023 American Physical Society. Received 7 July 2023. Accepted 11 October 2023. Published 6 November 2023.
• Created on: 2024-07-23 10:46:45