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 Heisenherg 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) similar or equal to N 0.147, and that the critical exponents of these quantities are beta/nu = 0.32 +/- 0.05 and gamma/nu = 1.86 +/- 0.15, respectively. These estimates result in a nontrivial dynamical critical exponent, z = 0.50 +/- 0.25.