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Let $\varphi\colon X\rightarrow Y$ be a degree two Galois cover of smoothcurves over a local field $F$ of odd characteristic. Assuming that $Y$ has goodreduction, we describe a semi-stability criterion for the curve $X$, using thedata of the branch locus of the covering $\varphi$. In the case that $X$ hassemi-stable reduction, we describe the dual graph of the minimal regular modelof $X$ over $F.$ We do this by adopting the notion of cluster picture definedfor hyperelliptic curves for the case where $Y$ is not necessarily a rationalcurve. Using these results, we describe the variation of the p-adic volume ofHitchin fibers over the semi-stable locus of the moduli space of rank 2 twistedHiggs bundles.

Cluster pictures for Hitchin fibers of rank two Higgs bundles