1999
DOI: 10.1103/physreva.60.1442
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Application of renormalization-group techniques to a homogeneous Bose gas at finite temperature

Abstract: A homogeneous Bose gas is investigated at finite temperature using renormalization group techniques. A non-perturbative flow equation for the effective potential is derived using sharp and smooth cutoff functions. Numerical solutions of these equations show that the system undergoes a second order phase transition in accordance with universality arguments. We obtain the critical exponent ν = 0.73 to leading order in the derivative expansion.

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Cited by 39 publications
(64 citation statements)
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“…It is however known that mean-field theory is not appropriate near the critical temperature because the fluctuations dominate the mean field in this region. This follows from applying the so-called Ginzburg criterion [4,5] and has triggered several attempts to go beyond mean-field theory near the critical region by means of various renormalization group (RG) techniques in the homogeneous interacting Bose gas [6,7,8,9,10,11,12]. This recent work was added to a significant amount of existing literature on the application of RG methods to interacting Bose gases, that was written when such systems were only an interesting theoretical problem [13,14,15,16,17,18].…”
Section: Introductionmentioning
confidence: 99%
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“…It is however known that mean-field theory is not appropriate near the critical temperature because the fluctuations dominate the mean field in this region. This follows from applying the so-called Ginzburg criterion [4,5] and has triggered several attempts to go beyond mean-field theory near the critical region by means of various renormalization group (RG) techniques in the homogeneous interacting Bose gas [6,7,8,9,10,11,12]. This recent work was added to a significant amount of existing literature on the application of RG methods to interacting Bose gases, that was written when such systems were only an interesting theoretical problem [13,14,15,16,17,18].…”
Section: Introductionmentioning
confidence: 99%
“…(2). In the homogeneous case the momentum-shell method has been explored extensively [6,7,8,9,10,11,12]. In the case we are dealing with here, the noninteracting Hamiltonian (g = 0) derived from (2) does not commute with the momentum operator because of the presence of the trapping potential.…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…The expectation is, that these irrelevant contributions are numerically small compared to the contribtutions originating from irrelevant terms of lower order vertices. In concrete terms, our truncation is as follows: When we calculate the flow of v l , we will consider irrelevant contributions fromΓ (8) l but ignore contributions fromΓ (10) l (in this case, there are in fact no second order terms arising from inhomogeneitiesΓ (n) l with n ≥ 10 so that we really have all second order terms included in our flow of v l ). Similarly, to calculate the flow of the four-point vertex parameters a l , b l , and u l , we ignore contributions arising fromΓ (8) l .…”
Section: Improved Description Of the Critical Regime In D = 3: Inmentioning
confidence: 99%
“…However, these methods are uncontrolled in the critical regime where one is faced with a strong-coupling problem. Renormalization group (RG) techniques are expected to perform better and several authors have ap-plied RG techniques to investigate the IR behavior of weakly interacting bosons [9,10,11], though no attempt was made to calculate the momentum dependence of the self-energy. Note that standard field theoretical RG is confined to the critical regime k ≪ k c .…”
Section: Introductionmentioning
confidence: 99%