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In this paper we give another proof of $p_c = \frac{\sqrt{q}}{1+\sqrt{q}}$ on$\mathbb{Z}^2$ with $q \in [1,4]$, based on the method of parafermionicobservables.

Another proof of $p_c = \frac{\sqrt{q}}{1+\sqrt{q}}$ on $\mathbb{Z}^2$ with $q \in [1,4]$ for random-cluster model