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

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.

(v2) Published in EPL, minor typos corrected, updated ancillary files, no change in results. (v1) 6 pages, 3 figures, 2 tables, ancillary file with results, LaTeX file with feynMF package

References in corpus (8)

• Hidden area and mechanical nonlinearities in freestanding graphene
• The effect of rippling on the mechanical properties of graphene
• Crumpled-to-tubule transition in anisotropic polymerized membranes: beyond epsilon-expansion
• Universal Elasticity and Fluctuations of Nematic Gels
• Anomalous elasticity of nematic elastomers
• Thermal fluctuations and anomalous elasticity of homogeneous nematic elastomers
• Nonlinear Elasticity, Fluctuations and Heterogeneity of Nematic Elastomers
• Phases and Transitions in Phantom Nematic Elastomer Membranes