We investigate the finite-volume critical behavior of an effective four-dimensional lattice scalar sector motivated by Higgs-like condensation. The scalar field studied in this work is treated as an effective order-parameter proxy for the scalar channel expected after Hubbard–Stratonovich bosonization of an underlying spinor-condensation mechanism. Using Hybrid Monte Carlo simulations, we identify a finite-volume critical window near κ ≈ 0.128, characterized by Binder-cumulant suppression, enhanced scalar susceptibility, and large integrated autocorrelation times consistent with critical slowing down. The results provide numerical evidence for finite-volume critical behavior in an effective scalar order-parameter sector. Rather than establishing a direct simulation of the underlying microscopic spinor dynamics, this work focuses on validating the effective scalar sector and its associated numerical diagnostics. The study serves as a computationally accessible validation step within a broader research program and establishes a stable numerical pipeline for future reduced-fermion and overlap-fermion simulations.
Jeong-Myung Jin (Mon,) studied this question.