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

We critically discuss the results reported in arXiv:2311.17994v1 by L. Oppenheim, M. Koch-Janusz, S. Gazit, and Z. Ringel, on the multicritical behavior of the three-dimensional Ising-Gauge model at the multicritical point. We argue that their results do not contradict the theoretical scenario put forward in “Multicritical point of the three-dimensional ℤ_2 gauge Higgs model”, Phys. Rev. B 105, 165138 (2022), arXiv:2112.01824, that predicted a multicritical behavior controlled by the stable XY fixed point of an effective three-dimensional ℤ_2⊕ℤ_2 Landau-Ginzburg-Wilson Φ^4 field theory. Actually, their results, as well as all numerical results reported so far in the literature, are consistent with a multicritical XY scenario.