Quantum Monte Carlo Study of the Two-dimensional Random Transverse-field Ising ferromagnet

Abstract

The random transverse-Field Ising ferromagnet(RTFIF) serves as a foundational model for random quantum spin systems. For the one-dimensional systems, its critical phenomena are understood to be governed by an infinite-randomness fixed point(IRFP). Similar assumptions have been extended to its two-dimensional counterpart, with a large body of research predicting the same governance by an IRFP. Despite this, a consensus on the exact critical properties remains elusive. In this work, extensive quantum Monte Carlo(QMC) simulations and finite-size scaling analysis were employed to investigate the precise critical behaviors of the 2D RTFIF. Furthermore, this study explores the impact of variations in transverse-field distribution on these critical phenomena. For the 2D RTFIF, the QMC predicts the critical point Γc = 7.52(2), with critical exponents β = 1.5(3), ν = 1.6(3), and z = 3.3(3) or ψ = 0.50(3), confirming existing results. However, contrary to common expectation, the McCoy-Wu model turns out to deviate from the 2D RTFIF universality class, yielding ΓMW = 1.57(1), β = 0.62(2), cν = 0.95(2), and z = 1.7(2) or ψ = 0.38(3). Rather, it aligns with the two-dimensional random Ising spin glass universality class. This implies that there exists more profound principle determining the critical properties in two dimension. This findings enhance our understanding of two-dimensional random quantum spin systems with Ising symmetry.