Renormalization-group study of a superconducting phase transition: Asymptotic behavior of higher expansion orders and results of three-loop calculations

Renormalization-group investigation of a superconducting U( r )-phase transition using five loops calculations

“…In our case K = 4 (five-loop approximation). Equations (15) can be solved in the form of ε-expansion with the formally small parameter ε. Similar to [14] we will consider numerical solution of the equations (15).…”

“…Equations (15) can be solved in the form of ε-expansion with the formally small parameter ε. Similar to [14] we will consider numerical solution of the equations (15). As usual, the ε-expansion in the right hand side of equations (15) is asymptotic expansion with zero radius of convergence.…”

“…Similar to [14] we will consider numerical solution of the equations (15). As usual, the ε-expansion in the right hand side of equations (15) is asymptotic expansion with zero radius of convergence. Then the equations (15) must be resummed to obtain results at physical points ε = 1 or ε = 2.…”

“…Such asymptotic behavior is called a higher-order asymptotic (HOA) and was investigated in [15] in the model considered.…”

“…Such a resummation requires knowing the higher orders asymptotics (HOA) of the ε expansion. The HOA of the considered model was determined in [15] using methods of instanton analysis [17]. The analysis and the results obtained are described briefly in Sec.…”