Renormalization-group calculation of the critical-point exponentηfor a critical point of arbitrary order

The critical-point exponent η for a critical point of order O in dimensions less than dO≡2O(O-1), is calculated to leading nonvanishing order in the parameter εO≡dO-d. The result is given for n-component isotropically interacting magnetic systems. For Ising systems, $n=1$, the result is ηO=εO²4(O-1)²(2OO)³. As O increases, the coefficient of εO² rapidly becomes very small, varying as 2^-6O for O large. In the limit of large n, ηO for odd order points approaches a constant and, for even order points, is proportional to 1/n.