Groundstate finite-size corrections and dilogarithm identities for the twisted $A_1^{(1)}$, $A_2^{(1)}$ and $A_2^{(2)}$ models

Alexi Morin-Duchesne, Andreas Klümper, Paul A. Pearce

We consider the $Y$-systems satisfied by the $A_1^{(1)}$, $A_2^{(1)}$, $A_2^{(2)}$ vertex and loop models at roots of unity with twisted boundary conditions on the cylinder. The ve…