We locate the phase-transition line for the Ising model on the fuzzy sphere from a finite-size scaling analysis of its ground-state energy. Our strategy is to write the latter as $E_{\mathrm{GS}}\left(N_m\right)/N_m=E_0+E_1/N_m+E_{3/2}/N_m^{3/2}+\cdots$ and to search for a minimum of $\chi :=E_{3/2}/E_0$ as a function of the couplings. Conformal perturbation theory predicts that around a conformal field theory, $\chi ={\chi }_{\min }+{\sum }_i{\lambda }_i^2{N}_m^{-{\omega }_i}+O\left({\lambda }^3\right)$, where ${\lambda }_i$ are the couplings associated with perturbations of operators with dimension ${\mathrm{\Delta }}_i$ and ${\omega }_i=d-{\mathrm{\Delta }}_i$. This procedure finds the critical curve of Zhu et al. [Phys. Rev. X 13, 021009 (2023)] and its sweet spot with good precision. Varying two coupling constants allows us to extract the correction-to-scaling exponent $\omega$ associated with the two leading scalars $\varepsilon$ and ${\varepsilon }^{\prime }$. We find similar results when normalizing by the gap to the stress tensor $T$ or the first parity-odd operator $\sigma$ instead of $E_0$.

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• Critical phenomena
• Phase transitions
• 3-dimensional systems
• Conformal field theory