2002/07/31 by Jean-Loı̈c Kneur, Jean-Loic Kneur, Marcus Benghi Pinto +2
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Physics of Superconductivity and Magnetism #Quantum, superfluid, helium dynamics #cond-mat.soft #cond-mat.stat-mech #hep-ph #hep-th
paper · pdf · doi:10.1103/physreva.68.043615
published as Phys.Rev. A68 (2003) 043615 · 38 pages, 3 eps figures, Revtex4. Final version in press Phys. Rev. A
arxiv created 2003/08/06 · openalex publication_date 2003/10/13 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We investigate the convergence properties of optimized perturbation theory, or linear \ensuremathδ expansion (LDE), within the context of finite temperature phase transitions. Our results prove the reliability of these methods, recently employed in the determination of the critical temperature Tc for a system of a weakly interacting homogeneous dilute Bose gas. We carry out explicit LDE optimized calculations and also the infrared analysis of the relevant quantities involved in the determination of Tc in the large-N limit, when the relevant effective static action describing the system is extended to O(N) symmetry. Then, using an efficient resummation method, we show how the LDE can already exactly reproduce the known large-N result for Tc at the first nontrivial order. Next, we consider the finite N=2 case where, using similar resummation techniques, we improve the analytical results for the nonperturbative terms involved in the expression for the critical temperature, allowing comparison with recent Monte Carlo estimates of them. To illustrate the method, we have considered a simple geometric series showing how the procedure as a whole works consistently in a general case.