Evaluating Critical Exponents in the Optimized Perturbation Theory

TL;DR

This paper applies optimized perturbation theory to evaluate critical exponents in the 3d O(N) scalar model, marking the first successful implementation of this method for such calculations and showing modest improvements over mean field results.

Contribution

It introduces a novel application of the linear delta expansion to compute critical exponents in the 3d O(N) model, with a detailed discussion of implementation subtleties and potential for higher-order accuracy.

Findings

Modest improvement over mean field values for eta and nu

Method shows potential to approach known critical exponents

First successful use of optimized perturbation theory in this context

Abstract

We use the optimized perturbation theory, or linear delta expansion, to evaluate the critical exponents in the critical 3d O(N) invariant scalar field model. Regarding the implementation procedure, this is the first successful attempt to use the method in this type of evaluation. We present and discuss all the associated subtleties producing a prescription which can, in principle, be extended to higher orders in a consistent way. Numerically, our approach, taken at the lowest nontrivial order (second order) in the delta expansion produces a modest improvement in comparison to mean field values for the anomalous dimension eta and correlation length nu critical exponents. However, it nevertheless points to the right direction of the values obtained with other methods, like the epsilon-expansion. We discuss the possibilities of improving over our lowest order results and on the convergence to the known values when extending the method to higher orders.