Renormalisation for Reaction-Diffusion Systems with Non-Local Interactions
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910076524036096 |
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| author | Greenman, Chris D |
| author_facet | Greenman, Chris D |
| contents | 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 $A_p+A_q\rightarrow ϕ$, and this process paired with branching, birth and death. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_02040 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Renormalisation for Reaction-Diffusion Systems with Non-Local Interactions Greenman, Chris D Mathematical Physics 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 $A_p+A_q\rightarrow ϕ$, and this process paired with branching, birth and death. |
| title | Renormalisation for Reaction-Diffusion Systems with Non-Local Interactions |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2601.02040 |