EXACT 5-LOOP RENORMALIZATION-GROUP FUNCTIONS OF PHI(4)-THEORY WITH O(N)-SYMMETRICAL AND CUBIC INTERACTIONS - CRITICAL EXPONENTS UP TO EPSILON(5)

The renormalization group functions are calculated in D = 4-epsilon dimensions for the phi(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; eta, nu, and omega are expanded up to order epsilon(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 greater than or equal to 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.