Exact correlation-length exponent for the clean Ashkin–Teller model on general regular lattices

Determine the exact correlation-length exponent [?] for the clean two-dimensional Ashkin–Teller model defined on a general regular lattice, where the critical line is not self-dual and the exact relation between the critical coupling and Coulomb-gas coupling is unavailable.

Background

The paper studies the Ashkin–Teller model on non-periodic lattices and uses the exact Coulomb-gas relations between the correlation-length exponent, anomalous dimensions, and coupling parameter as a benchmark for clean universality. On a self-dual square lattice, the critical line and the relation between the critical coupling and the Coulomb-gas coupling are known analytically. However, for a clean Ashkin–Teller model on a general regular lattice that is not self-dual, these lattice-specific relations are not available. Establishing them would provide an exact benchmark for interpreting numerical critical exponents on non-self-dual and disordered lattices.