The entropy conjecture for the multicritical point of the square-lattice 7 Ising model

Let $p_c$ be the probability of a ferromagnetic bond at the multicritical point of the square-lattice $7$ Ising model with quenched randomness. The bond distribution is therefore ferromagnetic with probability $p_c$ and antiferromagnetic with probability $1-p_c$.

Entropy conjecture. The exact location of the multicritical point is given by

$$-p_c\log p_c-(1-p_c)\log(1-p_c)=\frac{\log 2}{2}.$$

This is the zero-replica consequence proposed for the multicritical point on the Nishimori line. The source presents it as conjectural because the replica method and the required existence and analyticity assumptions are not formally proved.