The $\lambda$-point anomaly in view of the seven-loop Hypergeometric resummation for the critical exponent $\nu$ of the $O(2)$ ${\varphi }^4$ model

Abstract

In this work, we use a specific parameterization of the hypergeometric approximants ( the one by Mera et.al in Phys. Rev. Let. 115, 143001 (2015)) to approximate the seven-loop critical exponent $\nu$ for the $O(2)$-symmetric ${\varphi }^4$ model. Our prediction gives the result $\nu =0.6711(7)$ which is compatible with the value $\nu =0.6709(1)$ from the famous experiment carried on the space shuttle Columbia. On the other hand, our result is also compatible with recent precise theoretical predictions that are excluding the experimental result. These theoretical results include non-perturbative renormalization group calculations ( $\nu =0.6716(6)$), the most precise result from Monte Carlo simulations ($\nu =0.67169(7)$) as well as the recent conformal bootstrap calculations ($\nu =0.67175(10)$). Although our result is compatible with experiment, the plot of renormalization group result versus the number of loops suggests that higher orders are expected to add significantly to accuracy and precision of the $\nu$ exponent in a way that may favor the theoretical predictions.

References in corpus (4)

• Monte Carlo study of an improved clock model in three dimensions
• Monte Carlo study of a generalized icosahedral model on the simple cubic lattice
• Precise Critical Exponents of the O(N)-Symmetric Quantum field Model using Hypergeometric-Meijer Resummation
• Quantum critical properties of Bose-Hubbard models

Cited by in corpus (7)

• Precision calculation of universal amplitude ratios in $O(N)$ universality classes: Derivative Expansion results at order $\mathcal{O}({\partial }^4)$
• Conformal invariance and composite operators: A strategy for improving the derivative expansion of the nonperturbative renormalization group
• Extrapolation from hypergeometric functions, continued functions and Borel-Leroy transformation; Resummation of perturbative renormalization functions from field theories
• Conformal invariance constraints in the $O(N)$ models: a first study within the nonperturbative renormalization group
• High-Order Parametrization of the Hypergeometric-Meijer Approximants
• Continued functions and critical exponents: Tools for analytical continuation of divergent expressions in phase transition studies
• Continued functions and Borel-Leroy transformation: Resummation of six-loop ε-expansions from different universality classes