The renormalized thermal mass and critical temperature of a complex scalar field theory with non-zero charge density

Jones, H. F.; Parkin, Philip

doi:10.1016/s0550-3213(00)00662-3

Cited by 6 publications

(9 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Technically, as we shall see, this translates into extra difficulties due to the Hugenholtz-Pines theorem which washes out direct (tadpole) contributions, meaning that the first non-trivial contributions to φ 2 start at the three-loop level via two-loop self-energies. Apart from the quantum mechanical applications [21,22,23,24], the LDE was successfully applied to the description of mesoscopic systems [29], nuclear matter properties [27], phase transitions in the scalar λφ 4 model [30,31] as well as in the Gross-Neveu model [32], investigation of chiral symmetry phenomena in QCD [33] and in the determination of the equation of state for the Ising model [34]. It is worth mentioning that the application of the LDE to the scalar O(N ) × O(N ) model [35] has allowed to investigate the nonperturbative phenomenon of symmetry nonrestoration at high temperatures further than it was possible with other standard nonperturbative methods.…”

Section: A the Linear δ Expansionmentioning

confidence: 99%

Higher-order evaluation of the critical temperature for interacting homogeneous dilute Bose gases

et al. 2002

View full text Add to dashboard Cite

We use the nonperturbative linear δ expansion method to evaluate analytically the coefficients c1 and c ′′ 2 which appear in the expansion for the transition temperature for a dilute, homogeneous, three dimensional Bose gas given by Tc = T0{1+c1an 1/3 +[c ′ 2 ln(an 1/3 )+c ′′ 2 ]a 2 n 2/3 +O(a 3 n)}, where T0 is the result for an ideal gas, a is the s-wave scattering length and n is the number density. In a previous work the same method has been used to evaluate c1 to order-δ 2 with the result c1 = 3.06. Here, we push the calculation to the next two orders obtaining c1 = 2.45 at order-δ 3 and c1 = 1.48 at order-δ 4 . Analysing the topology of the graphs involved we discuss how our results relate to other nonperturbative analytical methods such as the self-consistent resummation and the 1/N approximations. At the same orders we obtain c ′′ 2 = 101.4, c ′′ 2 = 98.2 and c ′′ 2 = 82.9. Our analytical results seem to support the recent Monte Carlo estimates c1 = 1.32 ± 0.02 and c ′′ 2 = 75.7 ± 0.4.

show abstract

Section: A the Linear δ Expansionmentioning

confidence: 99%

Higher-order evaluation of the critical temperature for interacting homogeneous dilute Bose gases

et al. 2002

View full text Add to dashboard Cite

show abstract

“…For the interested reader Refs. [17,18,19,20,21,22,23,25,26,27,28,29,30,31,32,33] provide an extensive (but far from complete) list of successful applications of the method to different problems.…”

Section: Lde and The Interpolated Effective Scalar Theory For Becmentioning

confidence: 99%

“…An order-δ 2 application to ultra-relativistic gases has also been performed [19]. The LDE has been especially successful in treating scalar field theories at finite temperatures [20,21] as well as finite temperature and density [22]. Several different applications performed with the LDE are listed in Ref.…”

Section: Introductionmentioning

confidence: 99%

Asymptotically improved convergence of optimized perturbation theory in the Bose-Einstein condensation problem

2003

View full text Add to dashboard Cite

We investigate the convergence properties of optimized perturbation theory, or linear δ 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 weakly interacting homogeneous dilute Bose gas. We carry out the 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 exactly reproduce the known large-N result for Tc already at the first non-trivial 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.

show abstract

“…in units of the scale M, for T = 10.0, the A good test of our central result, the dimensional reduction, is to compare our formulae for the critical chemical potential with that extracted from the results of Jones and Parkin [12]. They also use the linear delta expansion but they apply it directly to the full fourdimensional theory anywhere in the symmetric phase.…”

Section: Discussionmentioning

confidence: 99%

“…We will use LDE, the Linear Delta Expansion, though the method is also known by several other names (see [20] for a brief summary). LDE has been used successfully in many situations, including studies of scalar theories at non-zero density such as [8,18,19,12,20]. In toy models, where exact results are achievable, LDE is known to produce convergent results and to do so much faster than alternatives, for instance see [21,22] and references therein.…”

Section: Linear Delta Expansionmentioning

confidence: 99%

Effect of weak interactions on the ultrarelativistic Bose-Einstein condensation temperature

Bedingham

Evans

2001

Phys. Rev. D

View full text Add to dashboard Cite

We calculate the ultra-relativistic Bose-Einstein condensation temperature of a complex scalar field with weak λ(Φ † Φ) 2 interaction. We show that at high temperature and finite density we can use dimensional reduction to produce an effective three-dimensional theory which then requires non-perturbative analysis. For simplicity and ease of implementation we illustrate this process with the linear delta expansion.

show abstract

The renormalized thermal mass and critical temperature of a complex scalar field theory with non-zero charge density

Cited by 6 publications

References 18 publications

Higher-order evaluation of the critical temperature for interacting homogeneous dilute Bose gases

Higher-order evaluation of the critical temperature for interacting homogeneous dilute Bose gases

Asymptotically improved convergence of optimized perturbation theory in the Bose-Einstein condensation problem

Effect of weak interactions on the ultrarelativistic Bose-Einstein condensation temperature

Contact Info

Product

Resources

About