CRITICAL EXPONENTS IN THE DELTA-EXPANSION

We investigate the possibility of using the logarithmic delta-expansion to calculate critical exponents by studying the standard example of a field theory showing a second-order phase transition: phi4 theory in three dimensions. Two approaches are explored. In the first an expansion about the free theory gives a fixed-point coupling of order 1/delta, so that infinitely many terms of the form delta(n)g(n) (when g is the coupling) have to be calculated to study the fixed-point structure of this system. In the second approach, the fixed point is of order delta, so that a systematic approximation scheme can be developed, but the leading-order corrections to the mean-field values of the exponents eta and nu are smaller than might be expected.