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We critically discuss the results reported in arXiv:2311.17994v1 by L.Oppenheim, M. Koch-Janusz, S. Gazit, and Z. Ringel, on the multicriticalbehavior of the three-dimensional Ising-Gauge model at the multicritical point.We argue that their results do not contradict the theoretical scenario putforward in ``Multicritical point of the three-dimensional ${\mathbb Z}_2$ gaugeHiggs model'', Phys. Rev. B 105, 165138 (2022), arXiv:2112.01824, thatpredicted a multicritical behavior controlled by the stable $XY$ fixed point ofan effective three-dimensional ${\mathbb Z}_2\oplus {\mathbb Z}_2$Landau-Ginzburg-Wilson $\Phi^4$ field theory. Actually, their results, as wellas all numerical results reported so far in the literature, are consistent witha multicritical $XY$ scenario.

Comment on "Machine Learning the Operator Content of the Critical Self-Dual Ising-Higgs Gauge Model'', arXiv:2311.17994v1