Renormalisation for Reaction-Diffusion Systems with Non-Local Interactions

Greenman, Christopher (2026) Renormalisation for Reaction-Diffusion Systems with Non-Local Interactions. Journal of Statistical Mechanics: Theory and Experiment, 2026 (4). p. 1. ISSN 1742-5468

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Abstract

Models of reaction diffusion processes usually employ discrete lattice models with particles interacting at the same site, resulting in localised reactions in the continuum limit. Here, various non-local interactions are considered, and two features reported. Firstly, it is shown that sufficiently non-local interactions will regulate ultra-violet divergences that perturbative methods with local interactions produce. However, in asymptotic regimes, infra-red divergences persist and ultra-violet divergences can reappear. Renormalisation methods are shown to report the same universal behaviour as local interactions at critical points. Secondly, the renormalisation group can be interpreted as a space-time-field rescaling that preserves action structure. This can be used to extract solutions to Callan–Symanzik equations directly without having to solve (or construct) the equation. These observations are exemplified for two paradigm models; annihilation (Formula presented) (Formula presented), and this process paired with branching, birth and death.

Item Type:	Article
Additional Information:	Publisher Copyright: © 2026 The Author(s). Published on behalf of SISSA Medialab srl by IOP Publishing Ltd. Original content from this work may be used under the terms of the https://creativecommons.org/licenses/by/4.0/. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Uncontrolled Keywords:	classical phase transitions,long-range interactions,renormalisation group,stochastic particle dynamics,statistical and nonlinear physics,statistics and probability,statistics, probability and uncertainty ,/dk/atira/pure/subjectarea/asjc/3100/3109
Faculty \ School:	Faculty of Science > School of Computing Sciences
UEA Research Groups:	Faculty of Science > Research Groups > Computational Biology Faculty of Science > Research Groups > Statistics
Related URLs:	https://www.scopus.com/pages/publication... https://arxiv.org/abs/2601.02040
Depositing User:	LivePure Connector
Date Deposited:	07 May 2026 09:38
Last Modified:	11 May 2026 13:06
URI:	https://ueaeprints.uea.ac.uk/id/eprint/102922
DOI:	10.1088/1742-5468/ae5c8c

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