Four-loop elasticity renormalization of low-temperature flat polymerized membranes

TL;DR

This paper performs a detailed four-loop renormalization analysis of flat polymerized membranes, providing precise estimates of critical exponents and confirming results across different models and experimental data.

Contribution

It offers the first complete four-loop perturbative renormalization of a low-temperature membrane model, enhancing accuracy of critical exponent predictions.

Findings

Analytical determination of the anomalous elasticity exponent η.

Results are apparently convergent series, enabling precise estimates.

Good agreement with non-perturbative theories and experimental data.

Abstract

We provide the complete four-loop perturbative renormalization of a low-temperature statistical mechanics model of flat polymerized membranes. Using a non-local effective flexural theory, which is based on transverse elastic fluctuations, we analytically determine the anomalous elasticity critical exponent $\eta$, which controls all scaling behaviors in the theory, at the four existing fixed points. The results are obtained as apparently convergent series, allowing for precise estimates without resummations. We independently verify and supplement the results of recent four-loop work [Pikelner 2022 EPL 138 17002] derived from a different model. Additionally, we find good agreement with non-perturbative theoretical approaches and experimental results on soft materials and graphene.