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Quantum Monte Carlo Study of Phase Diagram and Critical Phenomena of the Quantum Heisenberg Mattis Model in Two Dimensions

Ground-state properties of the two-dimensional S =1/2 Heisenberg Mattis model is investigated using the world-line quantum Monte Carlo method. Calculations of the spin glass order parameter show that the term proportional to L -2 is dominant in the scaling of this order parameter, and that this order parameter increases monotonously as the concentration of ferromagnetic bonds, p , is enhanced. Simulations of the Neel order parameter and the staggered susceptibility show that the Neel-Mattis spin glass phase boundary of the present model is consistent with the critical concentration of the two-dimensional Ising Mattis model, p c ≃0.147, and that the critical exponents of these quantities are β/ν=0.32±0.05 and γ/ν=1.86±0.15, respectively. These estimates result in a nontrivial dynamical critical exponent, z =0.50±0.25.