Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0512408 · Physical Review E

Universality and quantum effects in one-component critical fluids

Yves Garrabos

Published May 12, 2006• 7 citations
arXivHTMLPDF

Abstract

Nonuniversal scale transformations of the physical fields are extended to pure quantum fluids and used to calculate the susceptibility, the specific heat, and the order parameter density along the critical isochore of near its liquid-vapor critical point. Within the so-called preasymptotic domain, where the Wegner expansion restricted to the first term of confluent corrections to scaling is expected to be valid, the results are in agreement with the experimental measurements and recent predictions, either based on the minimal-substraction renormalization and the massive renormalization schemes within phi (4)(d = 3) (n = 1)the model, or based on the crossover parametric equation of state for Ising-like systems.

DOI
10.1103/physreve.73.056110

Related papers

Critical phenomena of fluids: Asymmetric Landau-Ginzburg-Wilson model

Jeffrey F. Nicoll

The critical behavior of simple single-component fluids near the liquid-vapor critical point (and of other systems in the same universality class) is examined via an asymmetric spin Hamiltonian in Landau-Ginzburg-Wilson form. The leading important odd terms to be added to an Ising-type system are a five-spin interaction $\ensuremath{\int}\ensuremath{\phi}^{5}(x)$ and a nonlocal cubic interaction $\ensuremath{-}\ensuremath{\int}\ensuremath{\phi}^{2}\ensuremath{\nabla}^{2}\ensuremath{\phi}$. These two operators can be combined into two different eigenoperators with distinct physical interpretations. One combination can be shown to be exactly equivalent to the mixing of field variables (e.g., chemical potential and temperature) in the temperaturelike variable of an Ising or Ising-type system. This mixing has been used phenomenologically, found in certain models, and justified on general geometric grounds. This is the first proof that all asymmetric models, assuming universality and barring accidents, will have such mixing; this implies the universal occurrence of a ${t}^{1\ensuremath{-}a}$ fluid diameter. The second combination is treated by renormalization-group methods and its contributions to the Helmholtz free energy, magnetic equation of state, and correlation length are calculated to $O({\ensuremath{\epsilon}}^{2}), \ensuremath{\epsilon}\ensuremath{\equiv}4\ensuremath{-}d$. There are several novel features of this interaction which persist to all orders in perturbation theory. In addition to the expected renormalized ${M}^{5}$ contribution to the free energy, there are also terms linear in $h$ (the magnetic field) and $M$ which could be described as nonanalytic fluctuation-induced shifts in the order parameter and field. These might appear experimentally as apparent shifts in the background terms for $h$ and $M$.

Physical Review A•Oct 1, 1981•149 citations

Non-Ising-like effects in the liquid-vapor transition: Equations of state

Chester A. Vause, Josef Sak

A Landau-Ginzburg-Wilson model is derived for a single-component fluid whose particles interact via a two-body potential. The effective Hamiltonian contains both even and odd powers in the order parameter (local fluid density). We study the effect of quintic interactions absent in the Ising model, and characterized by a new exponent ${\ensuremath{\varphi}}_{5}$, on various singular thermodynamic functions near the critical point. Mean-field, scaling, and renormalization-group (in $d=4\ensuremath{-}\ensuremath{\epsilon}$ dimensions) theories are used to evaluate the non-Ising effects due to ${\ensuremath{\varphi}}_{5}$. One of the main results of the asymmetry in this model is that it produces the leading singularity of the liquid-vapor coexistence diameter near the critical point: ${|t|}^{\ensuremath{\beta}\ensuremath{-}{\ensuremath{\varphi}}_{5}}$, where $\ensuremath{\beta}$ is the usual order-parameter exponent and $t$ is the reduced tem$\stackrel{\mathrm{\ifmmode \dot{}\else \.{}\fi{}}}{\mathrm{p}}$erature. The singularity ${|t|}^{1\ensuremath{-}\ensuremath{\alpha}}$ ($\ensuremath{\alpha}$ being the specific heat exponent) predicted by earlier phenomenological theories is not present in this theory. The problems associated with observing the non-Ising effects are briefly discussed.

Physical Review A•Jun 1, 1980•26 citations

Criticality and superfluidity in a dilute Bose fluid

Peter B. Weichman, Mark Rasolt, Michael Ellis Fisher +1 more

The crossover from ideal-Bose-gas behavior to nonclassical, XY-like criticality in a dilute, interacting Bose fluid is considered in detail with emphasis on the superfluid density, ${\ensuremath{\rho}}_{s}$(T), below the transition. A general discussion of crossover scaling in constrained systems shows that ${\ensuremath{\rho}}_{s}$ and other temperature-dependent thermodynamic functions at controlled overall density can be expressed in terms of universal scaling functions. The finite-temperature Green's function formalism is used to calculate the associated linear scaling fields and the crossover exponent exactly for all dimensionalities d>2, scaling predictions, including logarithmic singularities just at d=3, being checked via second-order computations. A mapping of the Bose problem onto the classical ${s}^{4}$ spin model is achieved which is asymptotically exact in the critical region. In this way, previously known renormalization-group results are used to calculate the scaling functions for ${\ensuremath{\rho}}_{s}$, for the off-diagonal susceptibility, etc., to first order in \ensuremath{\epsilon}=4-d. Good agreement is found with the experimental measurements by Reppy and co-workers of ${\ensuremath{\rho}}_{s}$(T) for helium absorbed at low coverages in Vycor glass (of pore size 50--80 A\r{}). An effective-mass ratio ${m}^{\mathrm{*}}$/m\ensuremath{\simeq}1.5, and an effective-scattering-length ratio ${a}^{\mathrm{*}}$/a\ensuremath{\simeq}1.3 are indicated for mobile helium in the Vycor (although the irregular character of Vycor has not, at this point, been fully allowed for in the theory). Other approaches in the literature to computing the critical behavior of quantum-mechanical systems are reviewed and related to the present analysis.

Physical review. B, Condensed matter•Apr 1, 1986•84 citations

Is the entropy at the liquid-gas critical point of pure fluids proportional to a master dimensionless constant ?

Yves Garrabos

From a minimal set made of four scale factors defined at the liquid-gas critical point of a pure fluid, and one adjustable parameter which accounts for particle quantum effects, we demonstrate here a master singular behavior of the correlation length for the one-component fluid subclass, using an asymptotic scale dilatation of the physical fields. Such master behavior observed within the preasymtotic domain is in conformity with the renormalized $Φ\_{d = 3}^{4}$ Field Theory predictions at large correlation length scale of the fluctuating order parameter, for the complete universality class of the symmetrical uniaxial 3D-Ising-like systems. The following consequences are discussed: (i) A comparison between the critical state of pure fluids and the zero-temperature state leads to an intuitive analogy with the (Nerst) third law of thermo- dynamics, which authorizes specific master form for hyperscaling within the subclass of pure fluids; (ii) A master constant value of the non-dimensional critical entropy can exist for all the pure fluids at the short-ranged lengthscale of the molecular interaction. From this latter hypothesis, we show that the needed four scale factors are the four preferred directions ex- pressing complete thermodynamic (linear) continuity crossing the liquid-gas critical point on the (pressure, volume, temperature) phase surface.

arXiv:cond-mat/0601088•Jan 5, 2006•2 citations

Nonasymptotic critical behavior from field theory atd=3. II. The ordered-phase case

C. Bagnuls, Claude Bervillier, Daniel I. Meiron +1 more

We present the first detailed calculations in the ordered phase using the massive ${\ensuremath{\varphi}}^{4}$ field theory directly at d=3. It is shown that an adapted expansion allows the renormalization functions of the symmetric theory to be kept unchanged. Extending results in a previous paper [C. Bagnuls and C. Bervillier, Phys. Rev. B 32, 7209 (1985)] (noted I), we obtain, for Ising-type systems, nonasymptotic functions of temperature for the spontaneous magnetization, the susceptibility, and the specific heat along the critical isochore, which include all the quantitative universal characteristics of critical behavior in the real preasymptotic critical domain ${D}_{\mathrm{preas}}$. All universal leading- and first-correction amplitude combinations (including the new one ${R}_{{B}_{{\mathrm{cr}}^{\mathrm{\ensuremath{-}}})}}$ are accurately estimated and are compared with previous theoretical and experimental estimates. We also show that the functions are well adapted to a suitable comparison with experiment and we describe how the adjustable parameters, limited to only three (the same as in I), enter in nonasymptotic critical behavior. Together with I, this work provides experimentalists with an efficient and coherent method which will facilitate the experimental test of the renormalization-group predictions.

arXiv:hep-th/0006187•Physical review. B, Condensed matter•Mar 1, 1987•193 citations

Classical-to-critical crossovers from field theory

C. Bagnuls, Claude Bervillier

We extend our previous determinations of nonasymptotic critical behavior of Phys. Rev. B 32, 7209 (1985) and 35, 3585 (1987) to accurate expressions of the complete classical-to-critical crossover (in three-dimensional field theory) in terms of the temperaturelike scaling field (i.e., along the critical isochore) for (1) the correlation length, the susceptibility, and the specific heat in the homogeneous phase for the n-vector model (n=1 to 3) and (2) the spontaneous magnetization (coexistence curve), the susceptibility, and the specific heat in the inhomogeneous phase for the Ising model (n=1). The present calculations include the seventh-loop order of Murray and Nickel and closely account for the up-to-date estimates of universal asymptotic critical quantities (exponents and amplitude combinations) provided by Guida and Zinn-Justin [J. Phys. A 31, 8103 (1998)].

arXiv:hep-th/0112209•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Jun 28, 2002•43 citations
Nonuniversal scale transformations of the physical fields are extended to pure quantum fluids and used to calculate the susceptibility, the specific heat, and the order parameter density along the critical isochore of near its liquid-vapor critical point. Within the so-called preasymptotic domain, where the Wegner expansion restricted to the first term of confluent corrections to scaling is expected to be valid, the results are in agreement with the experimental measurements and recent predictions, either based on the minimal-substraction renormalization and the massive renormalization schemes within phi (4)(d = 3) (n = 1)the model, or based on the crossover parametric equation of state for Ising-like systems.
The critical behavior of simple single-component fluids near the liquid-vapor critical point (and of other systems in the same universality class) is examined via an asymmetric spin Hamiltonian in Landau-Ginzburg-Wilson form. The leading important odd terms to be added to an Ising-type system are a five-spin interaction $\ensuremath{\int}\ensuremath{\phi}^{5}(x)$ and a nonlocal cubic interaction $\ensuremath{-}\ensuremath{\int}\ensuremath{\phi}^{2}\ensuremath{\nabla}^{2}\ensuremath{\phi}$. These two operators can be combined into two different eigenoperators with distinct physical interpretations. One combination can be shown to be exactly equivalent to the mixing of field variables (e.g., chemical potential and temperature) in the temperaturelike variable of an Ising or Ising-type system. This mixing has been used phenomenologically, found in certain models, and justified on general geometric grounds. This is the first proof that all asymmetric models, assuming universality and barring accidents, will have such mixing; this implies the universal occurrence of a ${t}^{1\ensuremath{-}a}$ fluid diameter. The second combination is treated by renormalization-group methods and its contributions to the Helmholtz free energy, magnetic equation of state, and correlation length are calculated to $O({\ensuremath{\epsilon}}^{2}), \ensuremath{\epsilon}\ensuremath{\equiv}4\ensuremath{-}d$. There are several novel features of this interaction which persist to all orders in perturbation theory. In addition to the expected renormalized M5{M}^{5}M5 contribution to the free energy, there are also terms linear in hhh (the magnetic field) and MMM which could be described as nonanalytic fluctuation-induced shifts in the order parameter and field. These might appear experimentally as apparent shifts in the background terms for hhh and MMM.
A Landau-Ginzburg-Wilson model is derived for a single-component fluid whose particles interact via a two-body potential. The effective Hamiltonian contains both even and odd powers in the order parameter (local fluid density). We study the effect of quintic interactions absent in the Ising model, and characterized by a new exponent ${\ensuremath{\varphi}}_{5}$, on various singular thermodynamic functions near the critical point. Mean-field, scaling, and renormalization-group (in $d=4\ensuremath{-}\ensuremath{\epsilon}$ dimensions) theories are used to evaluate the non-Ising effects due to ${\ensuremath{\varphi}}_{5}$. One of the main results of the asymmetry in this model is that it produces the leading singularity of the liquid-vapor coexistence diameter near the critical point: ${|t|}^{\ensuremath{\beta}\ensuremath{-}{\ensuremath{\varphi}}_{5}}$, where $\ensuremath{\beta}$ is the usual order-parameter exponent and ttt is the reduced tem$\stackrel{\mathrm{\ifmmode \dot{}\else \.{}\fi{}}}{\mathrm{p}}$erature. The singularity ${|t|}^{1\ensuremath{-}\ensuremath{\alpha}}$ ($\ensuremath{\alpha}$ being the specific heat exponent) predicted by earlier phenomenological theories is not present in this theory. The problems associated with observing the non-Ising effects are briefly discussed.
The crossover from ideal-Bose-gas behavior to nonclassical, XY-like criticality in a dilute, interacting Bose fluid is considered in detail with emphasis on the superfluid density, ${\ensuremath{\rho}}_{s}$(T), below the transition. A general discussion of crossover scaling in constrained systems shows that ${\ensuremath{\rho}}_{s}$ and other temperature-dependent thermodynamic functions at controlled overall density can be expressed in terms of universal scaling functions. The finite-temperature Green's function formalism is used to calculate the associated linear scaling fields and the crossover exponent exactly for all dimensionalities d>2, scaling predictions, including logarithmic singularities just at d=3, being checked via second-order computations. A mapping of the Bose problem onto the classical s4{s}^{4}s4 spin model is achieved which is asymptotically exact in the critical region. In this way, previously known renormalization-group results are used to calculate the scaling functions for ${\ensuremath{\rho}}_{s}$, for the off-diagonal susceptibility, etc., to first order in \ensuremath{\epsilon}=4-d. Good agreement is found with the experimental measurements by Reppy and co-workers of ${\ensuremath{\rho}}_{s}$(T) for helium absorbed at low coverages in Vycor glass (of pore size 50--80 A\r{}). An effective-mass ratio m∗{m}^{\mathrm{*}}m∗/m\ensuremath{\simeq}1.5, and an effective-scattering-length ratio a∗{a}^{\mathrm{*}}a∗/a\ensuremath{\simeq}1.3 are indicated for mobile helium in the Vycor (although the irregular character of Vycor has not, at this point, been fully allowed for in the theory). Other approaches in the literature to computing the critical behavior of quantum-mechanical systems are reviewed and related to the present analysis.
From a minimal set made of four scale factors defined at the liquid-gas critical point of a pure fluid, and one adjustable parameter which accounts for particle quantum effects, we demonstrate here a master singular behavior of the correlation length for the one-component fluid subclass, using an asymptotic scale dilatation of the physical fields. Such master behavior observed within the preasymtotic domain is in conformity with the renormalized Φ_d=34Φ\_{d = 3}^{4}Φ_d=34 Field Theory predictions at large correlation length scale of the fluctuating order parameter, for the complete universality class of the symmetrical uniaxial 3D-Ising-like systems. The following consequences are discussed: (i) A comparison between the critical state of pure fluids and the zero-temperature state leads to an intuitive analogy with the (Nerst) third law of thermo- dynamics, which authorizes specific master form for hyperscaling within the subclass of pure fluids; (ii) A master constant value of the non-dimensional critical entropy can exist for all the pure fluids at the short-ranged lengthscale of the molecular interaction. From this latter hypothesis, we show that the needed four scale factors are the four preferred directions ex- pressing complete thermodynamic (linear) continuity crossing the liquid-gas critical point on the (pressure, volume, temperature) phase surface.
We present the first detailed calculations in the ordered phase using the massive ${\ensuremath{\varphi}}^{4}$ field theory directly at d=3. It is shown that an adapted expansion allows the renormalization functions of the symmetric theory to be kept unchanged. Extending results in a previous paper [C. Bagnuls and C. Bervillier, Phys. Rev. B 32, 7209 (1985)] (noted I), we obtain, for Ising-type systems, nonasymptotic functions of temperature for the spontaneous magnetization, the susceptibility, and the specific heat along the critical isochore, which include all the quantitative universal characteristics of critical behavior in the real preasymptotic critical domain Dpreas{D}_{\mathrm{preas}}Dpreas​. All universal leading- and first-correction amplitude combinations (including the new one ${R}_{{B}_{{\mathrm{cr}}^{\mathrm{\ensuremath{-}}})}}$ are accurately estimated and are compared with previous theoretical and experimental estimates. We also show that the functions are well adapted to a suitable comparison with experiment and we describe how the adjustable parameters, limited to only three (the same as in I), enter in nonasymptotic critical behavior. Together with I, this work provides experimentalists with an efficient and coherent method which will facilitate the experimental test of the renormalization-group predictions.
We extend our previous determinations of nonasymptotic critical behavior of Phys. Rev. B 32, 7209 (1985) and 35, 3585 (1987) to accurate expressions of the complete classical-to-critical crossover (in three-dimensional field theory) in terms of the temperaturelike scaling field (i.e., along the critical isochore) for (1) the correlation length, the susceptibility, and the specific heat in the homogeneous phase for the n-vector model (n=1 to 3) and (2) the spontaneous magnetization (coexistence curve), the susceptibility, and the specific heat in the inhomogeneous phase for the Ising model (n=1). The present calculations include the seventh-loop order of Murray and Nickel and closely account for the up-to-date estimates of universal asymptotic critical quantities (exponents and amplitude combinations) provided by Guida and Zinn-Justin [J. Phys. A 31, 8103 (1998)].