Critical Casimir forces for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mi>N</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>models from functional renormalization

Jakubczyk, P.; Napiórkowski, Marcin

doi:10.1103/physrevb.87.165439

Cited by 12 publications

(18 citation statements)

References 55 publications

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“…It is the purpose of this paper to present a detailed exposition of the RG approach of [29] for the general case of a d-dimensional L 1 × L 2 · · · ×L d block geometry with L d ≡ L and the aspect ratios 4) and to further analyze the results. This includes applications to slab geometry (ρ α = L/L = ρ, α = 1, 2, ..., d−1) and a comparison with MC data [15,17,18,37,57] and with previous analytic work [14,23,[26][27][28]38]. A summary of our main results is given below.…”

Section: Introductionmentioning

confidence: 90%

“…(ii) As the bulk critical temperature T c is approached, long-range critical correlations occur for 1 ≤ n ≤ ∞ due to the divergence of the bulk correlation length [7] which implies massless critical modes of the bulk system right at T c . In a confining d-dimensional geometry of size L this leads to a critical Casimir force ∝ 1/L d at bulk T c [4,[12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][32][33][34][35][36][37][38][39]. This includes also systems with a onecomponent order parameter such as ordinary fluids [33], binary fluid mixtures [35], and Ising-like magnets [36,37].…”

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: Introductionmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

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 will be concerned with three different Bose gas models on a film [0, L] d−1 × [0, D]: the ideal Bose gas, the imperfect Bose gas model investigated in [23], [38], and [39], and the interacting Bose gas with n internal degrees of freedom in the limit n → ∞. In the case of the ideal Bose gas, the interaction u(x) is zero.…”

Section: E) Andmentioning

confidence: 99%

“…(3.37) can be computed by means of Mathematica [50]. One obtains 38) where 2F1 (a, b; c; z) is the regularized hypergeometric function 2 F 1 (a, b; c; z)/Γ(c). The result provides the analytic continuation to dimensions d ≥ 2.…”

Section: B Case Of Robin Boundary Conditionsmentioning

confidence: 99%

“…It can be obtained by taking the limit γ → 0 of a repulsive integrable Kac-type pair potential such as u γ (x) = γ d e −γx whose strength and inverse range are both controlled by the same parameter γ > 0 [23,38,39]. This is analogous to the well-known rigorous derivation of the van der Waals theory for a classical gas of particles interacting through an attractive Kac pair potential and a repulsive hard core [40], and hence reveals the mean-field nature of the approximation to which the model corresponds.…”

Section: E) Andmentioning

confidence: 99%

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Fluctuation-induced forces in confined ideal and imperfect Bose gases

Diehl

Rutkevich

2017

Phys. Rev. E

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Fluctuation-induced ("Casimir") forces caused by thermal and quantum fluctuations are investigated for ideal and imperfect Bose gases confined to d-dimensional films of size ∞ d−1 × D under periodic (P), antiperiodic (A), Dirichlet-Dirichlet (DD), Neumann-Neumann (NN), and Robin (R) boundary conditions (BCs). The full scaling functions, are determined for the ideal gas case with these BCs, where λ th and ξ are the thermal de-Broglie wavelength and the bulk correlation length, respectively. The associated limiting scaling functionsξ ) describing the critical behavior at the bulk condensation transition are shown to agree with those previously determined from a massive free O(2) theory for BC = P, A, DD, DN, NN. For d = 3, they are expressed in closed analytical form in terms of polylogarithms. The analogous scaling functions Υ BC d (x λ , x ξ , c1D, c2D) and Θ R d (x ξ , c1D, c2D) under the RBCs (∂z − c1)φ|z=0 = (∂z + c2)φ|z=D = 0 with c1 ≥ 0 and c2 ≥ 0 are also determined. The corresponding scaling functions Υ P ∞,d (x λ , x ξ ) and Θ P ∞,d (x ξ ) for the imperfect Bose gas are shown to agree with those of the interacting Bose gas with n internal degrees of freedom in the limit n → ∞. Hence, for d = 3, Θ P ∞,d (x ξ ) is known exactly in closed analytic form. To account for the breakdown of translation invariance in the direction perpendicular to the boundary planes implied by free BCs such as DDBCs, a modified imperfect Bose gas model is introduced that corresponds to the limit n → ∞ of this interacting Bose gas. Numerically and analytically exact results for the scaling function Θ DD ∞,3 (x ξ ) therefore follow from those of the O(2n) φ 4 model for n → ∞.

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Beyond N = ∞ in large N conformal vector models at finite temperature

Diatlyk,

Popov,

Wang

2024

J. High Energ. Phys.

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We investigate finite-temperature observables in three-dimensional large N critical vector models taking into account the effects suppressed by $$ \frac{1}{N} $$ 1 N . Such subleading contributions are captured by the fluctuations of the Hubbard-Stratonovich auxiliary field which need to be handled with care due to a subtle divergence structure which we clarify. The examples we consider include the scalar O(N) model, the Gross-Neveu model, the Nambu-Jona-Lasinio model and the massless Chern-Simons Quantum Electrodynamics. We present explicit results for the free energy density to the subleading order in $$ \frac{1}{N} $$ 1 N , which captures the thermal one-point function of the stress-energy tensor to this order. We also include the dependence on a chemical potential. We determine the Wilson coefficient in the thermal effective action that is sensitive to global symmetry for the first time directly in interacting CFTs, which produces a symmetry-resolved asymptotic density of states. We further provide a formula from diagrammatics for the one-point functions of general single-trace higher-spin currents. We observe that in most cases considered, these subleading effects lift the apparent degeneracies between observables in different models at infinite N, while in special cases the discrepancies only start to appear at the next-to-subleading order.

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Critical Casimir forces forO(N)models from functional renormalization

Cited by 12 publications

References 55 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

Fluctuation-induced forces in confined ideal and imperfect Bose gases

Beyond N = ∞ in large N conformal vector models at finite temperature

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