Evaluating Critical Exponents in the Optimized Perturbation Theory

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.

9 pages. Version with some corrections in relation to the published one

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Cited by in corpus (5)

• Emergence of Tricritical Point and Liquid-Gas Phase in the Massless 2+1 Dimensional Gross-Neveu Model
• Thermodynamics and Phase Structure of the Two-Flavor Nambu--Jona-Lasinio Model Beyond Large-N_c
• Critical and Tricritical Points for the Massless 2d Gross-Neveu Model Beyond Large N
• Applicability of the Linear delta Expansion for the lambda phi^4 Field Theory at Finite Temperature in the Symmetric and Broken Phases
• Reliability of the optimized perturbation theory in the 0-dimensional $O(N)$ scalar field model