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Mikhail Kompaniets

Publications and source records attributed to Mikhail Kompaniets.

5 recordsLinked to original sources
arXiv2022

Benchmarking the Ising Universality Class in $3 \le d < 4$ dimensions

The Ising critical exponents $\eta$, $\nu$ and $\omega$ are determined up to one-per-thousand relative error in the whole range of dimensions $3 \le d < 4$, using numerical conformal-bootstrap techniques. A detailed comparison is made with results by the resummed epsilon-expansion in varying dimension, the analytic bootstrap, Monte Carlo and non-perturbative renormalization-group methods, finding very good overall agreement. Precise conformal field theory data of scaling dimensions and structure constants are obtained as functions of dimension, improving on earlier findings, and providing benchmarks in $3 \le d < 4$.

hep-th↗
arXiv2021

Critical exponents from five-loop scalar theory renormalization near six-dimensions

We present five-loop results for the renormalization of various models with a cubic interaction (in ${d = 6 - 2 \varepsilon}$ dimensions). For the scalar model and its ${O(n)}$-symmetric extension we provide renormalization constants, anomalous dimensions and critical exponents. We discuss in detail the method of calculation, and provide all counterterms up to five loops. This allows one to consider generalizations of the ${\varphi^3}$ theory to other symmetries.

hep-th↗
arXiv2020

Fractal dimension of critical curves in the $O(n)$-symmetric $ϕ^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models

We calculate the fractal dimension $d_{\rm f}$ of critical curves in the $O(n)$ symmetric $(\vec ϕ^2)^2$-theory in $d=4-\varepsilon$ dimensions at 6-loop order. This gives the fractal dimension of loop-erased random walks at $n=-2$, self-avoiding walks ($n=0$), Ising lines $(n=1)$, and XY lines ($n=2$), in agreement with numerical simulations. It can be compared to the fractal dimension $d_{\rm f}^{\rm tot}$ of all lines, i.e. backbone plus the surrounding loops, identical to $d_{\rm f}^{\rm tot} = 1/ν$. The combination $ϕ_{\rm c}= d_{\rm f}/d_{\rm f}^{\rm tot} = νd_{\rm f}$ is the crossover exponent, describing a system with mass anisotropy. Introducing a novel self-consistent resummation procedure, and combining it with analytic results in $d=2$ allows us to give improved estimates in $d=3$ for all relevant exponents at 6-loop order.

cond-mat.stat-mech↗
arXiv2016

Renormalization group functions of $ϕ^4$ theory in the MS-scheme to six loops

Subdivergences constitute a major obstacle to the evaluation of Feynman integrals and an expression in terms of finite quantities can be a considerable advantage for both analytic and numeric calculations. We report on our implementation of the suggestion by F. Brown and D. Kreimer, who proposed to use a modified BPHZ scheme where all counterterms are single-scale integrals. Paired with parametric integration via hyperlogarithms, this method is particularly well suited for the computation of renormalization group functions and easily automated. As an application of this approach we compute the 6-loop beta function and anomalous dimensions of the $ϕ^4$ model.

hep-th↗