Possible determination of Exact Critical Exponents from three-dimensional Quantum Field Theory Abouzeid M. ShalabyDepartment of Physics and Materials Sciences, College of Arts and Sciences, Qatar University, P.O box 2713, Doha, Qatar

The λ-point dispute has been recognized in physics for over a decade. In the case of the superfluid phase transition of ⁴He, although Monte Carlo simulations and conformal field theory calculations yield highly precise results for the specific heat exponent, they do not align with experimental data. In Phys. Rev. D 102, 105017 (2020), we achieved significantly improved results for the renormalization group functions of the O (2)-symmetric ϕ⁴ field model (which is in the same class of universality with the ⁴He phase transition). These results are consistent with both experimental findings and Monte Carlo/conformal field theory calculations. To fully resolve the dispute, however, it is crucial to obtain exact critical exponents in three dimensions—something that has yet to be achieved by any method. Building on our recent work in Annals of Physics 470 (2024) 169786, we outline a roadmap for potentially deriving exact critical exponents from the low-order of the loop-expansion for the effective potential.