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Let $X$ be a compact Riemann surface. Let $(E,\theta)$ be a stable Higgsbundle of degree $0$ on $X$. Let $h_{\det(E)}$ denote a flat metric of thedeterminant bundle $\det(E)$. For any $t>0$, there exists a unique harmonicmetric $h_t$ of $(E,\theta)$ such that $\det(h_t)=h_{\det(E)}$. We prove thatif the Higgs bundle is induced by a line bundle on the normalization of thespectral curve, then the sequence $h_t$ is convergent to the naturally defineddecoupled harmonic metric at the speed of the exponential order. We also obtaina uniform convergence for such a family of Higgs bundles.

Asymptotic behaviour of large-scale solutions of Hitchin's equations in higher rank