Hybrid EFRG-DPIR approach to quantum criticality in the spin-1/2 transverse Ising model: Frustration effects on Tc and Ωc in 1D-3D lattices

We investigate the critical properties of the spin-S=1/2 transverse Ising model (TIM) on 1D linear, 2D honeycomb, square, Kagomé, and triangular, as well as 3D simple cubic lattices using a combined approach of the effective-field renormalization group (EFRG) method and the discretized path-integral representation (DPIR). This framework treats quantum fluctuations exactly within the path-integral formalism while incorporating cluster-based renormalization for accuracy beyond mean-field approximations. Applying this framework to 1D linear, 2D honeycomb, square, Kagomé, triangular, and 3D simple cubic lattices using finite clusters (N′=1,N=2), we compute critical temperatures Tc and quantum critical fields ϵc=Ωc/J as functions of transverse field strength. On frustrated Kagomé and triangular lattices, quantum fluctuations enhance spin-liquid stabilization and short-range correlations, contrasting robust ordering on bipartite linear, honeycomb, square, and simple cubic lattices. Our EFRG-DPIR approach achieves 3–8% accuracy compared to DMRG and quantum Monte Carlo benchmarks, significantly improving upon previous MFRG-DPIR estimates. The method successfully captures universality shifts toward spin-liquid phases in frustrated geometries, providing a powerful computational tool for exploring quantum phase transitions in complex magnetic systems.