Equation of state and critical exponents of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:mrow><mml:mprescripts /><mml:mrow /><mml:mrow><mml:mn>3</mml:mn></mml:mrow><mml:mrow /><mml:mrow /></mml:mmultiscripts></mml:mrow></mml:math>and a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:mrow

Pittman, Charles E.; Doiron, Theodore D.; Meyer, Horst

doi:10.1103/physrevb.20.3678

Cited by 80 publications

(19 citation statements)

References 32 publications

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“…This leads to a larger Ginzburg number and diminishes the deviations at higher t, but entails two undesirable consequences: Γ + lies certainly three standard deviations above the value quoted in Ref. [13] and a considerable part of the data at very small t has to be omitted from the analysis, even though there is no reason to expect stratification effects at these temperatures. With regard to the Ginzburg numbers found in our analysis, we note that the G + Xe /G + He > 1, whereas G − Xe /G − He (as obtained from the coexistence curve) lies much closer to unity; this is consistent with the corresponding first Wegner corrections, to which the Ginzburg parameter can be related, but seems to contradict the expected universality in the ratio of Ginzburg numbers above and below T c [29].…”

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confidence: 95%

“…These measurements used a volumetric method and join on smoothly to those of Ref. [13]. Below 1.4 K, ρ vap was obtained by using the ideal gas law as a reasonable approximation.…”

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confidence: 99%

“…Also for the coexistence curve ∆ρ * (−t) the results of Ref. [13] were used, where the density of both phases could be measured simultaneously. The range of the data was 3 × 10 −5 < −t 0.1 and could be extended by measurements of ρ liq at saturated vapor below 3.2 K (0.05 < −t < 1.0) [24], and of the vapor density ρ vap in equilibrium with the liquid above 1.4 K [25].…”

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confidence: 99%

“…For 3 He (P c = 1.168 bar, ρ c = 0.0414 g/cm 3 , T c = 3.317 K on the T 90 scale), compressibility data above T c were obtained from density measurements along isotherms over the range 0.05 < t 2 [21] and from measurements of the vertical density gradient in the gravitational field [13]. For the latter experiments, the determination of χ T is limited to the temperature range where the density gradient over the distance h is constant within the experimental error.…”

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confidence: 99%

“…7 of Ref. [13]), we use the individual liquid and vapor data in the form ∆ρ * + = (ρ liq − ρ c )/ρ c and ∆ρ…”

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confidence: 99%

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Crossover behavior in3Heand Xe near their liquid-vapor critical point

Luijten

Meyer

2000

Phys. Rev. E

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We present a detailed discussion of the crossover from mean-field to Ising critical behavior upon approach of the critical point, both for 3 He and Xe. By combining different sets of experimental data, we are able to cover an unusually large temperature range on either side of the critical temperature Tc. Below Tc, we thus can make an accurate comparison with a recent calculation for the crossover of the coexistence curve. For the regime above Tc, an analysis of the compressibility demonstrates that the crossover regime in 3 He is unexpectedly widened by a subtle interplay between quantum and critical fluctuations. 64.60.Fr, 05.70.Jk, 67.55.Cx Recently, there has been a renewed interest in the nature of the crossover from mean-field-like ("classical") to Isinglike critical behavior that occurs upon approach of the critical point. Although this phenomenon can be observed in a wide variety of experimental systems, including simple fluids, micellar solutions, and polymer mixtures, much of the recent attention has focused on its theoretical description. An important reason for this lack of experimental data is the width of the crossover region, which extends over several decades in the reduced temperature t ≡ (T − T c )/T c , where T c is the critical temperature. The crossover depends on the ratio between t and the (system-dependent) Ginzburg number G: Ising critical behavior occurs for t ≪ G and mean-field critical behavior is expected for t ≫ G. Throughout the crossover region, however, one has to stay within the critical regime, i.e., t 0.1. Hence, the full crossover can be observed only if G is sufficiently small. On the other hand, if G is extremely small, as for conventional superconductors which have G ≈ 10 −16 , the nonclassical region is so narrow that it becomes impossible to observe. Ideally, thus, one would need a system with a tunable Ginzburg number, as can actually be realized in polymer mixtures, where the Ginzburg number is inversely proportional to the molecular weight. Measurements of the crossover have indeed been reported for such systems [1,2], essentially confirming the existence of a crossover between the two universality classes. However, few studies have actually addressed the shape of the crossover curves. In Ref.[2] the concentration susceptibility χ as a function of t/G was shown to be well described by a phenomenological crossover function obtained by Belyakov and Kiselev (BK) [3], but it must be pointed out that χ increases by more than five orders of magnitude in the crossover region, making it difficult to judge even the qualitative agreement from a logarithmic plot. The effective susceptibility exponent, which is defined as the logarithmic derivative of χ,, is clearly a much more sensitive quantity. However, very few papers [5,6] have endeavored to discuss the shape of the crossover in experimental systems in terms of this parameter.It is the objective of this work to present an alternative description of experimental data exhibiting (part of) the crossover between mean-field-li...

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confidence: 95%

“…These measurements used a volumetric method and join on smoothly to those of Ref. [13]. Below 1.4 K, ρ vap was obtained by using the ideal gas law as a reasonable approximation.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

“…7 of Ref. [13]), we use the individual liquid and vapor data in the form ∆ρ * + = (ρ liq − ρ c )/ρ c and ∆ρ…”

mentioning

confidence: 99%

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