Quantum phase transitions in itinerant ferromagnets and the associated anomalous metallic behavior near quantum critical points constitute a central topic in condensed matter physics. In this work, we employ large-scale determinant quantum Monte Carlo simulations to investigate a two-dimensional fermion–Ising coupling model on a square lattice at half filling, in which itinerant electrons are longitudinally coupled to quantum Ising spins. We map out the complete temperature–transverse field ($T–h$) phase diagram and determine the ferromagnetic–paramagnetic phase boundary through a finite-size scaling analysis, yielding a ferromagnetic quantum critical point at $h_c=3.47\left(1\right)$ with a shift exponent $\psi =0.64\left(2\right)$. Assuming $z=1$, this shift exponent is consistent with the $(2+1)$-dimensional Ising universality class within error bars. In the paramagnetic regime above this quantum critical point, we observe a marginal Fermi-liquid phase characterized by linear-in-$T$ resistivity. We quantitatively determine, in large-scale numerical simulations, the crossover boundary from marginal Fermi-liquid to bad-metal behavior, defined by a dip in the local single-particle spectral function at the Fermi level. Multiple independent probes—including stochastic analytic continuation spectra, imaginary-time Green's function midpoint values, specific heat peaks, self-energy crossings, and direct-current resistivity minima—consistently cross-validate this crossover boundary. We further suggest that bad-metal behavior is plausibly governed by strong short-range antiferromagnetic fluctuations enhanced by Fermi-surface nesting, while persistently large double occupancy across the crossover region is less indicative of conventional Mott-type charge localization as the dominant mechanism.

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• Quantum phase transitions
• Strongly correlated systems
• Quantum Monte Carlo