Connections between the Critical Behavior of the Planar Model and That of the Eight-Vertex Model

Lines of critical points which emerge from the two-dimensional planar model's multicritical point are analyzed. These lines seem to be in the same universality class as both the Ashkin-Teller and the eight-vertex (8V) models' critical lines, with the multicritical point being isomorphic with the 8V model at both the points $tanh2\lambda =\frac{\sqrt{2}}{2} \mathrm{and} -1\mathrm{}$. Expansions of critical indices about these values of $\lambda$ are performed. If this analysis is right, then this work permits the evaluation of a whole class of interesting correlation functions at the critical point of the $F$ model and that of the four-state Potts model.