2026/05/31 by Hyeon Jung Kim, Seung-Jong Yoo, Jinmo Bok +3
Physics and Astronomy · #cond-mat.str-el
Completely rewritten and fine-tuned
arxiv created 2026/08/05 · arxiv updated 2026/08/06
We present a Renormalization Group (RG) framework based on a nonlocal effective action ansatz to analyze the strong coupling dynamics of the three-dimensional relativistic ϕ4 theory. By implementing a Hubbard-Stratonovich transformation, we decouple the quartic interaction into the primary field ϕ and an auxiliary field φ∼ ϕ2, allowing both exponents Δϕ and Δφ to act as independent, unconstrained variables rather than fixed scaling dimensions. Within this nonlocal propagator framework, both the field self-energies and vertex corrections are evaluated at the one-loop order. The resulting one-loop logarithmic derivatives determine the renormalization group flows of the couplings and the scaling exponents. For d=3 and ε≈-0.198, the self-consistent equations yield a representative fixed point at Δϕ≈0.97714, Δφ≈-0.65260, and Δϕ2≈1.04573, corresponding to ηϕ≈0.04572 and ν≈0.51170. Relative to the high-precision conformal-bootstrap benchmarks, the deviations are approximately 0.48% for Δϕ, 25.97% for Δϕ2, and 18.77% for ν, demonstrating sub-percent agreement in the fundamental-field sector while revealing substantially larger deviations in the composite and correlation-length sectors within the leading-order truncation.