One-dimensional sums and finitized characters of 2 × 2 fused RSOS models

Abstract

Tartaglia and Pearce have argued that the nonunitary fused Forrester–Baxter models are described, in the continuum scaling limit, by the minimal models constructed as the higher-level conformal cosets at integer fusion level and fractional level with . These results rely on Yang–Baxter integrability and are valid in Regime III for models determined by the crossing parameter in the interval . Combinatorially, Baxter’s one-dimensional sums generate the finitized branching functions as weighted walks on the Dynkin diagram. The ground state walks terminate within shaded n-bands, consisting of n contiguous shaded 1-bands. The shaded 1-bands occur between heights where , . These results do not extend to the interval since, for these models, there are no shaded n bands to support the ground states. Here we consider the models in the interval and investigate the associated one-dimensional sums. In this interval, we verify that the one-dimensional sums produce new finitized Virasoro characters of the minimal models with . We further conjecture finitized bosonic forms and check that these agree with the ground state one-dimensional sums out to system sizes N = 12. The models thus realize new Yang–Baxter integrable models in the universality classes of the minimal models . For the series with , the spin-1 one-dimensional sums were previously analysed by Jacob and Mathieu without the underlying Yang–Baxter structure. Finitized Kac characters for the logarithmic minimal models are also obtained for by taking the logarithmic limit with .