Determine the nature of the merged critical point and possible Hopf-defect condensation

Determine whether the merged critical point of the symmetric, antiferromagnetic, and symmetric-mass-generation phases is a multicritical point that describes a phase consisting of condensed topological defects.

Background

The paper studies a four-dimensional lattice Higgs model containing two massless staggered fermion fields coupled to an adjoint scalar field. Numerical simulations identify a weak-coupling massless symmetric phase, an intermediate antiferromagnetic phase, and a strong-coupling symmetric-mass-generation phase. The two critical lines bordering the antiferromagnetic phase appear to merge at a unique point where fermion bilinear condensates vanish while fermion susceptibilities exhibit nontrivial finite-size scaling.

The authors interpret this merged point as a possible multicritical point and speculate that it may correspond to a phase in which Hopf defects of the scalar field condense without breaking the model's global symmetries. The numerical evidence does not establish either the multicritical nature of the point or the proposed defect-condensed interpretation.