Exact five-loop renormalization group functions of θ4-theory with O( N)-symmetric and cubic interactions. Critical exponents up to ϵ5

Abstract

The renormalization group functions are calculated in D = 4 − ϵ dimensions for the θ 4-theory with two coupling constants associated with an O( N)-symmetric and a cubic interaction. Divergences are removed by minimal subtraction. The critical exponents η, ν, and ω are expanded up to order ϵ 5 for the three nontrivial fixed points O( N)-symmetric, Ising, and cubic. The results suggest the stability of the cubic fixed point for N ≥ 3, implying that the critical exponents seen in the magnetic transition of three-dimensional cubic crystals are of the cubic universality class. This is in contrast to earlier three-loop results which gave N > 3, and thus Heisenberg exponents. The numerical differences, however, are less than a percent making an experimental distinction of the universality classes very difficult.