Rogers-Ramanujan identities in Statistical Mechanics

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Bibliographic Details
Main Author:	Campbell, Geoffrey B.
Format:	Preprint
Published:	2024
Subjects:	Mathematical Physics Combinatorics History and Overview Number Theory 11P84 (primary), 37K60, 82B23 (secondary)
Online Access:	Acceder al recurso
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_version_	1866909201632067584
author	Campbell, Geoffrey B.
author_facet	Campbell, Geoffrey B.
contents	We describe the story of the Rogers-Ramanujan identities; being known for 85 years and having about 130 pure mathematics proofs, suddenly entering physics when Rodney Baxter solved the Hard Hexagon Model in Statistical Mechanics in 1980. We next cover the accompanying proofs by George E Andrews of other related Baxter identities arisen of Rogers-Ramanujan type, leading into a new flourishing partnership of Physics and Mathematics. Our narrative goes into the subsequent 44 years, explaining the progress in physics and mathematical analysis. Finally we show some related crossovers with regard to the Elliptic q-gamma function and some Vector Partition generating functional equations; the latter of which may be new. The present paper is essentially chapter 11 of a 32 chapter book to appear in June 2024.
format	Preprint
id	arxiv_https___arxiv_org_abs_2405_08425
institution	arXiv
publishDate	2024
record_format	arxiv
spellingShingle	Rogers-Ramanujan identities in Statistical Mechanics Campbell, Geoffrey B. Mathematical Physics Combinatorics History and Overview Number Theory 11P84 (primary), 37K60, 82B23 (secondary) We describe the story of the Rogers-Ramanujan identities; being known for 85 years and having about 130 pure mathematics proofs, suddenly entering physics when Rodney Baxter solved the Hard Hexagon Model in Statistical Mechanics in 1980. We next cover the accompanying proofs by George E Andrews of other related Baxter identities arisen of Rogers-Ramanujan type, leading into a new flourishing partnership of Physics and Mathematics. Our narrative goes into the subsequent 44 years, explaining the progress in physics and mathematical analysis. Finally we show some related crossovers with regard to the Elliptic q-gamma function and some Vector Partition generating functional equations; the latter of which may be new. The present paper is essentially chapter 11 of a 32 chapter book to appear in June 2024.
title	Rogers-Ramanujan identities in Statistical Mechanics
topic	Mathematical Physics Combinatorics History and Overview Number Theory 11P84 (primary), 37K60, 82B23 (secondary)
url	https://arxiv.org/abs/2405.08425

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