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arXiv · 2601.02040

Renormalisation for Reaction-Diffusion Systems with Non-Local Interactions

Chris D Greenman
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Abstract

Models of reaction diffusion processes usually employ discrete lattice models with particles interacting at the same site, resulting in localized 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 $A_p+A_q\rightarrow \phi$, and this process paired with branching, birth and death.

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Chris D Greenman. 2026-01-05. Renormalisation for Reaction-Diffusion Systems with Non-Local Interactions. https://arxiv.org/abs/2601.02040

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