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Fixed point structure of the Abelian Higgs model

G. Fejős^*

T. Hatsuda^†

Research Center for Nuclear Physics, Osaka University, Ibaraki, Osaka 567-0047, Japan and Theoretical Research Division, Nishina Center, RIKEN, Wako 351-0198, Japan

Theoretical Research Division, Nishina Center, RIKEN, Wako 351-0198, Japan and iTHES Research Group, RIKEN, Wako 351-0198, Japan

^*fejos@rcnp.osaka-u.ac.jp
^†thatsuda@riken.jp

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Phys. Rev. D 93, 121701(R) – Published 7 June, 2016

DOI: https://doi.org/10.1103/PhysRevD.93.121701

Abstract

The order of the superconducting phase transition is analyzed via the functional renormalization group approach. For the first time, we derive fully analytic expressions for the $β$ functions of the charge and the self-coupling in the Abelian Higgs model with one complex scalar field in $d = 3$ dimensions that support the existence of two charged fixed points: an infrared (IR) stable fixed point describing a second-order phase transition and a tricritical fixed point controlling the region of the parameter space that is attracted by the former one. It is found that the region separating first- and second-order transitions can be uniquely characterized by the Ginzburg-Landau parameter $κ$ , and the system undergoes a second-order transition only if $κ > κ_{c} \approx 0.62 / \sqrt{2}$ .

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Fixed point structure of the Abelian Higgs model

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