Erratum: Minimal renormalization without ε-expansion: Four-loop free energy in three dimensions for general n above and below T_{c} [Phys. Rev. E 67, 056115 (2003)]

Strösser, M.; Dohm, V.

doi:10.1103/physreve.70.069902

Cited by 9 publications

(21 citation statements)

References 3 publications

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“…The absence of Goldstone singularities is expected on general grounds [62] for O(n)-symmetric quantities (such as free energy, square of the order parameter, specific heat) in contrast to the true physical divergencies of the transverse and longitudinal susceptibilities for h → 0 [9]. Spurious singularities at intermediate stages of perturbation theory for the Gibbs free energy below T c are known to appear at higher order which, however, have been shown to cancel among themselves [9][10][11].…”

Section: A)mentioning

confidence: 99%

“…The nonanalytic dependence of g b,s on r 0T through r d/2 0T leads to divergencies in the derivatives of the free energy arising from the Goldstone modes for r 0T → 0 [9][10][11].…”

Section: A)mentioning

confidence: 99%

“…with an arbitrary inverse reference length µ. In view of the application to finite systems, we are using r rather than the bulk correlation lengths above and below T c ξ ± [11] as the appropriate measure of the temperature variable. Using r rather than ξ ± is advantageous in our finite-size theory where a single analytic finite-size scaling function is derived for the whole temperature regime −∞ ≤ r ≤ ∞.…”

Section: B Renormalizationmentioning

confidence: 99%

“…Both types of fluctuations exist in O(n)-symmetric systems undergoing a secondorder phase transition which is governed by the thermodynamic fluctuations of an n-component order parameter. (For bulk theories on systems with Goldstone modes near T c see, e.g., [8][9][10][11]). Examples of confined O(n)symmetric systems where both types of thermodynamic Casimir forces have been found or predicted to exist are superfluids (n = 2) [12,13], superconductors (n = 2) [14], XY magnets (n = 2) [15][16][17][18], isotropic Heisenberg magnets (n = 3) [15], spherical model systems with n = ∞ [19][20][21][22][23][24][25] as well as O(n)-symmetric ϕ 4 models with n ≥ 2 [26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

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Crossover from low-temperature to high-temperature fluctuations: Universal and nonuniversal Casimir forces of isotropic and anisotropic systems

Dohm

2018

Phys. Rev. E

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We study the crossover from low-temperature to high-temperature fluctuations including Goldstone-dominated and critical fluctuations in confined isotropic and weakly anisotropic O(n)-symmetric systems on the basis of a finite-size renormalization-group approach at fixed dimension d introduced previously [V. Dohm, Phys. Rev. Lett. 110, 107207 (2013)PRLTAO0031-900710.1103/PhysRevLett.110.107207]. Our theory is formulated within the φ^{4} lattice model in a d-dimensional block geometry with periodic boundary conditions. We calculate the finite-size scaling functions F^{ex} and X of the excess free-energy density and the thermodynamic Casimir force, respectively, for 1≤n≤∞, 20 and for film geometry (ρ=0). Good overall agreement is found with Monte Carlo (MC) data for isotropic spin models with n=1,2,3. For ρ=0, the low-temperature limits of F^{ex} and X vanish for n=1, whereas they are finite for n≥2. For ρ>0 and n=1, we find a finite low-temperature limit of F^{ex}, which deviates from that of the Ising model. We attribute this deviation to the nonuniversal difference between the φ^{4} model with continuous variables and the Ising model with discrete variables. For n≥2 and ρ>0, a logarithmic divergence of F^{ex} in the low-temperature limit is predicted, in excellent agreement with MC data. For 2≤n≤∞ and ρ<ρ_{0}=0.8567 the Goldstone modes generate a negative low-temperature Casimir force that vanishes for ρ=ρ_{0} and becomes positive for ρ>ρ_{0}. For anisotropic systems a unified hypothesis of multiparameter universality is introduced for both bulk and confined systems. The dependence of their scaling functions on d(d+1)/2-1 microscopic anisotropy parameters implies a substantial reduction of the predictive power of the theory for anisotropic systems as compared to isotropic systems. An exact representation is derived for the nonuniversal large-distance behavior of the bulk correlation function of anisotropic systems and quantitative predictions are made. The validity of multiparameter universality is proven analytically for the d=2,n=1 universality class. A nonuniversal anisotropy-dependent minimum of the Casimir force scaling function X is found. Both the sign and magnitude of X and the shift of the film critical temperature are affected by the lattice anisotropy.

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Section: A)mentioning

confidence: 99%

“…The nonanalytic dependence of g b,s on r 0T through r d/2 0T leads to divergencies in the derivatives of the free energy arising from the Goldstone modes for r 0T → 0 [9][10][11].…”

Section: A)mentioning

confidence: 99%

Section: B Renormalizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Crossover from low-temperature to high-temperature fluctuations: Universal and nonuniversal Casimir forces of isotropic and anisotropic systems

Dohm

2018

Phys. Rev. E

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“…is a universal quantity [52,53]. It is clear that if one considers ∆C µ ξ 3 0 as an approximation to an universal number, in line with Eq.…”

Section: Discussion and Concluding Remarksmentioning

confidence: 94%

Exact solution for the order parameter profiles and the Casimir force in 4He superfluid films in an effective field theory

Dantchev

Rudnick

Vassilev

et al. 2019

Physica A: Statistical Mechanics and its Applications

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We present an analytical solution of an effective field theory which, in one of its formulations, is equivalent to the Ginzburg's Ψ-theory for the behavior of the Casimir force in a film of 4 He in equilibrium with its vapor near the superfluid transition point. We consider three versions of the theory, depending on the way one determines its parameters from the experimental measurements. We present exact results for the behavior of the order parameter profiles and of the Casimir force within this theory, which is characterized by d = 3, ν = 2/3 and β = 1/3, where d is the bulk spatial dimension and ν and β are the usual critical exponents. In addition, we revisit relevant experiments [1] and [2] in terms of our findings. We find reasonably good agreement between our theoretical predictions and the experimental data. We demonstrate analytically that our calculated force is attractive. The position of the extremum is predicted to be at x min = π, with x = (L/ξ 0 )(T/T λ − 1) 1/ν , which value effectively coincides with the experimental finding x min = 3.2 ± 0.18. Here L is the thickness of the film, T λ is the bulk critical temperature and ξ 0 is the correlation length amplitude of the system for temperature T > T λ . The theoretically predicted position of the minimum does not depend on the one adjustable parameter, M, entering the theory. The situation is different with respect to the largest absolute value of the scaling function, which depends on both ξ 0 and on M. For this value the experiments yield −1.30. If one uses ξ 0 = 1.63 Å, as in the original Ψ theory of Ginsburg, one obtains the closest approach to the experimental value −1.848 with M = 0. If one uses M = 0.5, as inferred from other experiments, along with the best currently accepted experimental value for ξ 0 , ξ 0 = 1.432 Å, then the maximum value of the force is predicted to be −1.58. The effective theory considered here is not consistent with critical point universality; furthermore it incorrectly predicts ordering in the film in violation of known rigorous results. These issues are discussed in the text. vasilvas@imbm.bas.bg and padjon@imbm.bas.bg (and Peter A Djondjorov)

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Critical dynamics: a field-theoretical approach

Folk

Moser

2006

J. Phys. A: Math. Gen.

144

241

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Erratum: Minimal renormalization without ε-expansion: Four-loop free energy in three dimensions for general n above and below T_{c} [Phys. Rev. E 67, 056115 (2003)]

Cited by 9 publications

References 3 publications

Crossover from low-temperature to high-temperature fluctuations: Universal and nonuniversal Casimir forces of isotropic and anisotropic systems

Crossover from low-temperature to high-temperature fluctuations: Universal and nonuniversal Casimir forces of isotropic and anisotropic systems

Exact solution for the order parameter profiles and the Casimir force in 4He superfluid films in an effective field theory

Critical dynamics: a field-theoretical approach

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