Selection of stable fixed points by the Toledano-Michel symmetry criterion: Six-component example

Hatch, Dorian M.; Stokes, Harold T.; Kim, Jai Sam; Felix, Jefferey W.

doi:10.1103/physrevb.32.7624

Cited by 13 publications

(16 citation statements)

References 11 publications

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“…The bound [56] determines the radius of convergence of the ε-expansion. At the fixed point βλ (λ * ) = 4 ε − 12 Nλ * , (6.11) 12 An equivalent expression is given in appendix A of [55]. 13 This counting is the minimal form agreeing with explicit results up to six loops and satisfying the consistency conditions N (N λ) p−1 N which is positive for N ε < 36 π 2 and vanishes when N ε = 36 π 2 .…”

Section: Scalar Theories In 3 − ε Dimensionsmentioning

confidence: 80%

Seeking fixed points in multiple coupling scalar theories in the ε expansion

Osborn

Stergiou

2018

J. High Energ. Phys.

173

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Fixed points for scalar theories in 4 − ε, 6 − ε and 3 − ε dimensions are discussed. It is shown how a large range of known fixed points for the four dimensional case can be obtained by using a general framework with two couplings. The original maximal symmetry, O(N ), is broken to various subgroups, both discrete and continuous. A similar discussion is applied to the six dimensional case. Perturbative applications of the a-theorem are used to help classify potential fixed points. At lowest order in the ε-expansion it is shown that at fixed points there is a lower bound for a which is saturated at bifurcation points. arXiv:1707.06165v7 [hep-th]

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Section: Scalar Theories In 3 − ε Dimensionsmentioning

confidence: 80%

Seeking fixed points in multiple coupling scalar theories in the ε expansion

Osborn

Stergiou

2018

J. High Energ. Phys.

173

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show abstract

“…Under the assumption of a single quadratic invariant, an extensive analysis of fixed points was performed in [21] for N = 4, and in [22][23][24] for N = 6. These works identified dozens of fixed points, corresponding to various discrete subgroups of O(4) and O(6), respectively.…”

Section: Classification Resultsmentioning

confidence: 99%

General properties of multiscalar RG Flows in $d=4-\varepsilon$

2019

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Fixed points of scalar field theories with quartic interactions in d = 4 − ε dimensions are considered in full generality. For such theories it is known that there exists a scalar function A of the couplings through which the leading-order beta-function can be expressed as a gradient. It is here proved that the fixed-point value of A is bounded from below by a simple expression linear in the dimension of the vector order parameter, N . Saturation of the bound requires a marginal deformation, and is shown to arise when fixed points with the same global symmetry coincide in coupling space.Several general results about scalar CFTs are discussed, and a review of known fixed points is given.Dedicated to the memory of Louis Michel , the first IHES professor of physics and a pioneer of group theory applications to RG flows.

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“…The choice of H depends on the particular physical system for which critical exponents are to be found. For N = 4 [23,24] and N = 6 [25][26][27] detailed investigations for all possible subgroups of O(N ), the corresponding spaces of quartic polynomials and associated fixed points was undertaken. Further analysis for low N in 4 − ε and 3 − ε dimensions based on the symmetry groups for regular solids was described in [28].…”

Section: Jhep04(2021)128mentioning

confidence: 99%

Heavy handed quest for fixed points in multiple coupling scalar theories in the ε expansion

Osborn

Stergiou

2021

J. High Energ. Phys.

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The tensorial equations for non trivial fully interacting fixed points at lowest order in the ε expansion in 4 − ε and 3 − ε dimensions are analysed for N-component fields and corresponding multi-index couplings λ which are symmetric tensors with four or six indices. Both analytic and numerical methods are used. For N = 5, 6, 7 in the four-index case large numbers of irrational fixed points are found numerically where ‖λ‖2 is close to the bound found by Rychkov and Stergiou [1]. No solutions, other than those already known, are found which saturate the bound. These examples in general do not have unique quadratic invariants in the fields. For N ⩾ 6 the stability matrix in the full space of couplings always has negative eigenvalues. In the six index case the numerical search generates a very large number of solutions for N = 5.

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Selection of stable fixed points by the Toledano-Michel symmetry criterion: Six-component example

Cited by 13 publications

References 11 publications

Seeking fixed points in multiple coupling scalar theories in the ε expansion

Seeking fixed points in multiple coupling scalar theories in the ε expansion

General properties of multiscalar RG Flows in $d=4-\varepsilon$

Heavy handed quest for fixed points in multiple coupling scalar theories in the ε expansion

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