Accurate critical exponents from field theory

J.C. Le Guillou , J. Zinn-Justin

This is the third article in a sequence in which we reexamine the calculation of the critical exponents of the N-vector model from field theory. In the first article we have applied summation methods to the ε-expansion for which new terms have been calculated (up to order ε5). In the second article we have incorporated in the summation method, in the case of Ising-like systems (N = 1), the knowledge of the exact values of exponents in d = 2 dimensions. Since exact values are now also known in the case of polymers (N = 0), we apply here the same method to this case. Moreover, since for the exponent η for N = 1 the results coming from the ε-expansion and perturbation series at fixed dimension are slightly different, we have recalculated the exponents in the latter case using the variant of the summation method developed for the ε-expansion. The results do not change significantly showing both the reliability and the limits of the method.

Mots clés: axiomatic field theory; Ising model; perturbation theory

Domaines: Articles anciens

J.C. Le Guillou, J. Zinn-Justin. Accurate critical exponents from field theory. Journal de Physique, 1989, 50 (12), pp.1365-1370. ⟨10.1051/jphys:0198900500120136500⟩. ⟨jpa-00211001⟩