Power law singularities in n-vector models

Power law singularities and critical exponents in n-vector models are considered within a theoretical approach called GFD (grouping of Feynman diagrams) theory. It is discussed how possible values of the critical exponents can be related to specific n-vector models in this approach. A good agreement with the estimates of the perturbative renormalization group (RG) theory can be obtained. Predictions for corrections to scaling of the perturbative RG and GFD approaches are different. A nonperturbative proof is provided, supporting corrections to scaling of the GFD theory. Highly accurate experimental data very close to the λ-transition point in liquid helium, as well as the Goldstone mode singularities in n-vector spin models, evaluated from Monte Carlo simulation results, are discussed with an aim to test the theoretical predictions. Our analysis shows that in both cases the data can be well interpreted within GFD theory. (author)