Lattice models and generalized Rogers Ramanujan identities

TL;DR

This paper revisits solvable lattice models, deriving generalized Rogers Ramanujan identities through a new method that confirms some conjectures and introduces new identities, linking statistical models with number theory.

Contribution

The paper provides a novel proof technique for local state probabilities in lattice models, leading to new and confirmed Rogers Ramanujan identities.

Findings

Derived generalized Rogers Ramanujan identities

Provided proofs for some conjectured identities

Generated new identities beyond previous conjectures

Abstract

We revisit the solvable lattice models described by Andrews Baxter and Forrester and their generalizations. The expressions for the local state probabilities were shown to be related to characters of the minimal models. We recompute these local state probabilities by a different method. This yields generalized Rogers Ramanujan identities, some of which recently conjectured by Kedem et al. Our method provides a proof for some cases, as well as generating new such identities.