For all coprime (p,p'), the dense A_1^(1) and dilute A_2^(2) loop models are conjectured to have identical torus conformal partition functions, supporting a common logarithmic universality class.
Nienhuis, Exact critical point and critical exponents of O(n) models in two dimensions , Phys
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Modular covariant torus partition functions of dense $A_1^{(1)}$ and dilute $A_2^{(2)}$ loop models
For all coprime (p,p'), the dense A_1^(1) and dilute A_2^(2) loop models are conjectured to have identical torus conformal partition functions, supporting a common logarithmic universality class.