Spectral renormalization group for the Gaussian model and ${\ensuremath{\psi}}^{4}$ theory on nonspatial networks

Spectral renormalization group for the Gaussian model and $ψ^{4}$ theory on nonspatial networks

Aslı Tuncer and Ayşe Erzan

Phys. Rev. E 92, 022106 – Published 6 August 2015; Erratum Phys. Rev. E 98, 019901 (2018)

Abstract

We implement the spectral renormalization group on different deterministic nonspatial networks without translational invariance. We calculate the thermodynamic critical exponents for the Gaussian model on the Cayley tree and the diamond lattice and find that they are functions of the spectral dimension, $\tilde{d}$ . The results are shown to be consistent with those from exact summation and finite-size scaling approaches. At $\tilde{d} = 2$ , the lower critical dimension for the Ising universality class, the Gaussian fixed point is stable with respect to a $ψ^{4}$ perturbation up to second order. However, on generalized diamond lattices, non-Gaussian fixed points arise for $2 < \tilde{d} < 4$ .

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Received 26 December 2013
Revised 3 April 2015

DOI:https://doi.org/10.1103/PhysRevE.92.022106

Erratum

Erratum: Spectral renormalization group for the Gaussian model and $ψ^{4}$ theory on nonspatial networks [Phys. Rev. E 92, 022106 (2015)]

Aslı Tuncer and Ayşe Erzan

Phys. Rev. E 98, 019901 (2018)

Authors & Affiliations

Aslı Tuncer^1,2 and Ayşe Erzan¹

¹Department of Physics, Istanbul Technical University, Maslak 34469, Istanbul, Turkey
²Department of Physics, Işık University, Şile 34980, Istanbul, Turkey

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Vol. 92, Iss. 2 — August 2015

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Physical Review E

covering statistical, nonlinear, biological, and soft matter physics

Spectral renormalization group for the Gaussian model and $ψ^{4}$ theory on nonspatial networks

Aslı Tuncer and Ayşe Erzan

Phys. Rev. E 92, 022106 – Published 6 August 2015; Erratum Phys. Rev. E 98, 019901 (2018)

Abstract

Erratum

Erratum: Spectral renormalization group for the Gaussian model and $ψ^{4}$ theory on nonspatial networks [Phys. Rev. E 92, 022106 (2015)]

Aslı Tuncer and Ayşe Erzan

Phys. Rev. E 98, 019901 (2018)

Authors & Affiliations

Article Text (Subscription Required)

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Physical Review E

covering statistical, nonlinear, biological, and soft matter physics

Spectral renormalization group for the Gaussian model and ψ4 theory on nonspatial networks

Aslı Tuncer and Ayşe Erzan

Phys. Rev. E 92, 022106 – Published 6 August 2015; Erratum Phys. Rev. E 98, 019901 (2018)

Abstract

Erratum

Erratum: Spectral renormalization group for the Gaussian model and ψ4 theory on nonspatial networks [Phys. Rev. E 92, 022106 (2015)]

Aslı Tuncer and Ayşe Erzan

Phys. Rev. E 98, 019901 (2018)

Authors & Affiliations

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Spectral renormalization group for the Gaussian model and $ψ^{4}$ theory on nonspatial networks

Erratum: Spectral renormalization group for the Gaussian model and $ψ^{4}$ theory on nonspatial networks [Phys. Rev. E 92, 022106 (2015)]