Functional Relations in Solvable Lattice Models II

TL;DR

This paper applies the $T$-system functional relations to compute correlation lengths and central charges in solvable lattice models, confirming and extending known results across different regimes.

Contribution

It demonstrates the effectiveness of the $T$-system in deriving key physical quantities for models based on simple Lie algebras, generalizing previous findings.

Findings

Correlation lengths determined for massive vertex models in anti-ferroelectric regime

Central charges calculated for RSOS models in critical regimes

Results reproduce and extend known values

Abstract

Reported are two applications of the functional relations ($T$-system) among a commuting family of row-to-row transfer matrices proposed in the previous paper Part I. For a general simple Lie algebra $X_r$, we determine the correlation lengths of the associated massive vertex models in the anti-ferroelectric regime and central charges of the RSOS models in two critical regimes. The results reproduce known values or even generalize them, demonstrating the efficiency of the $T$-system.