Multicritical behavior of the two-field Ginzburg–Landau model coupled to a gauge field

In this paper, we study the multicritical behavior of the Ginzburg–Landau model in a O(n1)⊕O(n2)O(n1)⊕O(n2)-symmetric version containing (n1/2+n2/2)(n1/2+n2/2)-complex order parameters coupled to a gauge field. We develop the RG analysis at a one-loop approximation in the context of the ϵϵ-expansion approach. The beta functions are obtained, and in the case of equal couplings between the two scalar fields and the gauge field and n1=n2=n/2n1=n2=n/2, the infrared stability of the fixed points is discussed. It is found that the charged infrared-stable fixed point exists for n>393.2n>393.2. Calculations of the relevant critical exponents are also carried out.