Analyticity of critical exponents of the $O(N)$ models from nonperturbative renormalization

@article{Chlebicki2020AnalyticityOC,
  title={Analyticity of critical exponents of the \$O(N)\$ models from nonperturbative renormalization},
  author={Andrzej Chlebicki and Paweł Jakubczyk},
  journal={arXiv: Statistical Mechanics},
  year={2020}
}
We employ the functional renormalization group framework at second order in the derivative expansion to study the $O(N)$ models continuously varying the number of field components $N$ and the spatial dimensionality $d$. Of our special interest are phenomena occurring in the vicinity of $d=2$. We in particular address the Cardy-Hamber prediction concerning nonanalytical behavior of the critical exponents $\nu$ and $\eta$ across a line in the $(d,N)$ plane, which passes through the point $(2,2… 

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References

SHOWING 1-10 OF 55 REFERENCES
Precision calculation of critical exponents in the O(N) universality classes with the nonperturbative renormalization group.
TLDR
A determination of critical exponents of O(N) models for various values of N is obtained with a precision which is similar or better than those obtained by most field-theoretical techniques and reaches a better precision than Monte Carlo simulations in some physically relevant situations.
Nonperturbative renormalization group treatment of amplitude fluctuations for |φ | 4 topological phase transitions
The study of the Berezinskii-Kosterlitz-Thouless transition in two-dimensional ${|\ensuremath{\varphi}|}^{4}$ models can be performed in several representations, and the amplitude-phase (AP) Madelung
Dual lattice functional renormalization group for the Berezinskii-Kosterlitz-Thouless transition: Irrelevance of amplitude and out-of-plane fluctuations.
TLDR
A functional renormalization group (FRG) approach for the two-dimensional XY model is developed by combining the lattice FRG proposed by Machado and Dupuis with a duality transformation that explicitly introduces vortices via an integer-valued field, demonstrating that previous failures to obtain a line of true fixed points within the FRG are a mathematical artifact of insufficient truncation schemes.
Critical exponents of O (N ) models in fractional dimensions
We compute critical exponents of O(N) models in fractal dimensions between two and four, and for continuos values of the number of field components N, in this way completing the RG classification of
Nonperturbative renormalization flow and essential scaling for the Kosterlitz-Thouless transition
The Kosterlitz-Thouless phase transition is described by the nonperturbative renormalization flow of the two-dimensional ${\ensuremath{\varphi}}^{4}$ model. The observation of essential scaling
Quantum field theory in the large N limit: a review
Abstract We review the solutions of O ( N ) and U ( N ) quantum field theories in the large N limit and as 1/ N expansions, in the case of vector representations. Since invariant composite fields
The nonperturbative functional renormalization group and its applications
The renormalization group plays an essential role in many areas of physics, both conceptually and as a practical tool to determine the long-distance low-energy properties of many systems on the one
Longitudinal fluctuations in the Berezinskii-Kosterlitz-Thouless phase
We analyze the interplay of longitudinal and transverse fluctuations in a $U(1)$ symmetric two-dimensional $\phi^4$-theory. To this end, we derive coupled renormalization group equations for both
Unified picture of ferromagnetism, quasi-long-range order, and criticality in random-field models.
TLDR
The interplay between ferromagnetism, quasi-long-range order (QLRO), and criticality in the d-dimensional random-field O(N) model in the whole (N, d) diagram is studied.
Variational resummation for ϵ-expansions of critical exponents of nonlinear O(n)-symmetric σ-model in 2+ϵ dimensions
We develop a method for extracting accurate critical exponents from perturbation expansions of the On -symmetric nonlinear s-model in Ds 2 q e dimensions. This is possible by considering the
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