2004/06/11 by Marcus Benghi Pinto, Rudnei O. Ramos, Paulo J. Sena
Physics and Astronomy · #Physics of Superconductivity and Magnetism #Quantum Chromodynamics and Particle Interactions #Theoretical and Computational Physics #cond-mat.other #hep-th
paper · pdf · doi:10.1016/j.physa.2004.05.042
published as Physica A342 (2004) 570 · 9 pages. Version with some corrections in relation to the published one
openalex publication_date 2004/06/11 · arxiv created 2004/10/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.