Characterization of the additional multicritical fixed point

Determine the nature and global fixed-point properties of the additional Abelian Higgs fixed point with three unstable directions that is reported to collide with the bicritical charged fixed point $C_-$ near $N\simeq 9.5$ in three dimensions.

Background

The paper finds that, in three dimensions, the charged fixed point C−C_- with two relevant directions undergoes a collision near N≃9.5N\simeq 9.5 with another fixed point having three unstable directions. The additional fixed point is not characterized within the analysis, and its existence and properties are important for understanding the multicritical fixed-point structure and the failure of conventional large-NN scaling in the three-dimensional Abelian Higgs model.

References

While the structure seen in Fig. \ref{fig:fpsketch} remains for $1.5\lesssim N\lesssim 9.5$, we find that when increasing $N$ from $N_c(d=3)\simeq 1.5$, around $N\simeq9.5$, $C_-$ collides with another, yet unknown FP with three unstable directions and disappears.

— Global Fixed Point Potentials in the Abelian Higgs Model with $N$ flavors  (2609.04938 - Fejős et al., 4 Sep 2026) in Section V, Numerical fixed point solutions