Five loop renormalization of ${\varphi }^3$ theory with applications to the Lee-Yang edge singularity and percolation theory

Abstract

We apply the method of graphical functions that was recently extended to six dimensions for scalar theories, to ${\varphi }^3$ theory and compute the $\beta$ function, the wave function anomalous dimension as well as the mass anomalous dimension in the $\overline{\mbox{MS}}$ scheme to five loops. From the results we derive the corresponding renormalization group functions for the Lee-Yang edge singularity problem and percolation theory. After determining the $\epsilon$ expansions of the respective critical exponents to $\mathcal{O}({\epsilon }^5)$ we apply recent resummation technology to obtain improved exponent estimates in 3, 4 and 5 dimensions. These compare favourably with estimates from fixed dimension numerical techniques and refine the four loop results. To assist with this comparison we collated a substantial amount of data from numerical techniques which are included in tables for each exponent.

54 pages, 15 figures; v2: additional summary tables and references added - version to be published in PRD

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• Graphical functions in even dimensions
• Universal location of Yang-Lee edge singularity for a one-component field theory in $1\le d\le 4$
• Resonant resurgent asymptotics from quantum field theory
• Universal location of Yang-Lee edge singularity in classic O(N) universality classes
• Renormalization and non-renormalization of scalar EFTs at higher orders
• Ginzburg-Landau Description and Emergent Supersymmetry of the $(3,8)$ Minimal Model
• Model A of critical dynamics: 5-loop $\epsilon$ expansion study
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• Recursive computation of Feynman periods
• Worldline description of a bi-adjoint scalar and the zeroth copy
• Field-theoretic analysis of directed percolation: Three-loop approximation
• Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: ${\varphi }^3$ QFT in 6 Dimensions
• Is there supersymmetric Lee-Yang fixed point in three dimensions?
• Site and bond percolation on four-dimensional simple hypercubic lattices with extended neighborhoods
• The analytic structure of three-point functions from contour deformations
• Flow-oriented perturbation theory
• The two upper critical dimensions of the Ising and Potts models
• Critical Field Theories with OSp$(1|2M)$ Symmetry
• Testing the RG-flow $M(3,10)+{\varphi }_{1,7}\to M(3,8)$ with Hamiltonian Truncation
• Entanglement dynamics in monitored Kitaev circuits: loop models, symmetry classification, and quantum Lifshitz scaling
• Experimental validation of nonextensive statistical field theory: applications to manganites
• Percolation in a simple cubic lattice with distortion
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• Noise Effects on Pade Approximants and Conformal Maps
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• Field-theoretic Analysis of Dynamic Isotropic Percolation: Three-loop Approximation
• Anomalous dimensions at small spins
• Nonextensive percolation and Lee-Yang edge singularity from nonextensive $\lambda {\varphi }^3$ scalar field theory
• Is ${\gamma }_{KLS}$-generalized statistical field theory complete?
• A universality class for RNA-like polymers and double polymers
• A detailed field theory for RNA-like molecules with periodic base sequence
• On the completeness of the ${\delta }_{KLS}$-generalized statistical field theory
• Extended-range percolation in five dimensions
• Critical and multicritical Lee-Yang fixed points in the local potential approximation