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Journal of the Physical Society of Japan

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

Yoshihiko Nonomura

Published Sep 15, 1997• 0 citations
Publisher

Abstract

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 Néel order parameter and the staggered susceptibility show that the Néel-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.

DOI
10.1143/jpsj.66.2638

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The two-dimensional S = 1/2 asymmetric Heisenberg Mattis model is investigated with the exact diagonalization of finite clusters. The Néel order parameter and the spin glass order parameter can be smoothly extrapolated to the thermodynamic limit in the antiferromagnetic region, as in the pure Heisenberg antiferromagnet. The critical concentration of the Néel phase is consistent with that of the two-dimensional Ising Mattis model, and the spin glass order parameter increases monotonously as the ferro-bond concentration increases. These facts suggest that quantum fluctuation does not play an essential role in two-dimensional non-frustrated random spin systems.
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In order to gain a deeper understanding of the quantum criticality in the explicitly staggered dimerized Heisenberg models, we study a generalized staggered dimer model named the J 0 — J 1 — J 2 model, which corresponds to the staggered J — J ′ model on a square lattice and a honeycomb lattice when J 1 / J 0 equals 1 and 0, respectively. Using the quantum Monte Carlo method, we investigate all the quantum critical points of these models with J 1 / J 0 changing from 0 to 1 as a function of coupling ratio α = J 2 / J 0 . We extract all the critical values of the coupling ratio α c for these models, and we also obtain the critical exponents ν, β/ν, and η using different finite-size scaling ansätz,. All these exponents are not consistent with the three-dimensional Heisenberg universality class, indicating some unconventional quantum critical points in these models.