Frequency regulators for the nonperturbative renormalization group: A general study and the model A as a benchmark

Duclut, Charlie; Delamotte, Bertrand

doi:10.1103/physreve.95.012107

Cited by 39 publications

(57 citation statements)

References 57 publications

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“…Furthermore, it is also found that the dynamical critical exponent in a relativistic O(N ) vector model is close to 2 [63]. Similar result is also found for the O(3) model in [75]. In summary, whether the critical dynamics of the relativistic O(4) scalar theory falls into Model A or Model G is still an open question, and more insightful studies are required.…”

Section: Dynamical Critical Exponentsupporting

confidence: 69%

“…But if the regulator in Equation ( 17) is extended to the one having a finite imaginary part, as done in some nonequilibrium calculations, e.g. [75], a nonvanishing qq-component of regulators is necessary. With the regulator in Equation ( 21), one can reformulate the flow equation for the effective action in Equation (113) as such…”

Section: The O(n ) Scalar Theory Within the Real-time Frg Approachmentioning

confidence: 99%

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Real-time dynamics of the $O(4)$ scalar theory within the fRG approach

Tan¹,

Chen²,

2022

SciPost Phys.

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In this paper, the real-time dynamics of the O(4)O(4) scalar theory is studied within the functional renormalization group formulated on the Schwinger-Keldysh closed time path. The flow equations for the effective action and its nn-point correlation functions are derived in terms of the "classical'' and "quantum’’ fields, and a concise diagrammatic representation is presented. An analytic expression for the flow of the four-point vertex is obtained. Spectral functions with different values of temperature and momentum are obtained. Moreover, we calculate the dynamical critical exponent for the phase transition near the critical temperature in the O(4)O(4) scalar theory in 3+13+1 dimensions, and the value is found to be z\simeq 2.023z≃2.023.

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Section: Dynamical Critical Exponentsupporting

confidence: 69%

Section: The O(n ) Scalar Theory Within the Real-time Frg Approachmentioning

confidence: 99%

Real-time dynamics of the $O(4)$ scalar theory within the fRG approach

Tan¹,

Chen²,

2022

SciPost Phys.

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“…However, in the range 1/4 ≤ θ < 1/2, an ambiguity arises in the second term, since this term vanishes only if the limit → 0 is taken before the integration on ω. This ambiguity is present because the frequency sector is not properly regularized, and would disappear with a frequency-dependent regulator [62]. Since the result should not depend on the choice of the regulator, we simply assume that this term is zero since it would vanish with a frequency regulator.…”

Section: Discussionmentioning

confidence: 99%

Kardar-Parisi-Zhang equation with temporally correlated noise: A nonperturbative renormalization group approach

Squizzato

Canet

2019

Phys. Rev. E

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We investigate the universal behavior of the Kardar-Parisi-Zhang equation with temporally correlated noise. The presence of time correlations in the microscopic noise breaks the statistical tilt symmetry, or Galilean invariance, of the original KPZ equation with delta-correlated noise (denoted SR-KPZ). Thus it is not clear whether the KPZ universality class is preserved in this case. Conflicting results exist in the literature, some advocating that it is destroyed even in the limit of infinitesimal temporal correlations, while others find that it persists up to a critical range of such correlations. Using non-perturbative and functional renormalization group techniques, we study the influence of two types of temporal correlators of the noise: a short range one with a typical time-scale τ , and a power-law one with a varying exponent θ. We show that for the short-range noise with any finite τ , the symmetries (the Galilean symmetry, and the time-reversal one in D = 1 + 1) are dynamically restored at large scales, and the long-distance properties are governed by the SR-KPZ fixed point. In the presence of a power-law noise, we find that the SR-KPZ fixed point is still stable for θ below a critical value θc, in accordance with previous RG results, while a long-range (LR) fixed-point controls the critical scaling for θ > θc, and we evaluate the θ-dependent critical exponents at this LR fixed point, in both D = 1 + 1 and D = 2 + 1 dimensions. While the results in D = 1 + 1 can be compared to previous estimates, no other prediction was available in D = 2 + 1.

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“…The process is the same as above, except that the temperature immediately after t = 0 is now the Curie temperature: In this situation, the correlation length still grows as a power law, ξ(t) ∼ t 1 /zc , with z c ≈ 2.17 the critical dynamical exponent [52,13,53,54]. The growth of the correlation length is slightly slower than in the previous situation since 1 /z c ≈ 0.461 < 1 /2.…”

Section: Quench To T = T Cmentioning

confidence: 95%

Critical percolation in the slow cooling of the bi-dimensional ferromagnetic Ising model

Ricateau¹,

Cugliandolo²,

Picco³

2018

J. Stat. Mech.

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We study, with numerical methods, the fractal properties of the domain walls found in slow quenches of the kinetic Ising model to its critical temperature. We show that the equilibrium interfaces in the disordered phase have critical percolation fractal dimension over a wide range of length scales. We confirm that the system falls out of equilibrium at a temperature that depends on the cooling rate as predicted by the Kibble -Zurek argument and we prove that the dynamic growing length once the cooling reaches the critical point satisfies the same scaling. We determine the dynamic scaling properties of the interface winding angle variance and we show that the crossover between critical Ising and critical percolation properties is determined by the growing length reached when the system fell out of equilibrium. arXiv:1709.05268v1 [cond-mat.stat-mech] 15 Sep 2017Since the interfaces on short length scales are not smooth anymore, their fractal dimension is given bywhere κ c = 3 is the same universal parameter as in the pre-factor in front of the logarithmic growth of the wav. Note that D c/z c ≈ 0.634 > 1 /2. The wav still has a universal behaviour, now highlighted

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Frequency regulators for the nonperturbative renormalization group: A general study and the model A as a benchmark

Cited by 39 publications

References 57 publications

Real-time dynamics of the $O(4)$ scalar theory within the fRG approach

Real-time dynamics of the $O(4)$ scalar theory within the fRG approach

Kardar-Parisi-Zhang equation with temporally correlated noise: A nonperturbative renormalization group approach

Critical percolation in the slow cooling of the bi-dimensional ferromagnetic Ising model

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