Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Ground-State Phase Diagrams of the Two-Dimensional Quantum Heisenberg Spin Glass Models

Yoshihiko Nonomura, Yukiyasu Ozeki

Published Jan 1, 1995• 5 citations
OpenAlex

Abstract

Ground-state properties of the two-dimensional S = 1/2 random Heisenberg models are investigated by the exact-diagonalization method. The phase diagram of the bondrandom model (the ±J model) is the same as that of the corresponding Ising spin glass model, in spite of quantum fluctuation. In the site-random model, the spin glass phase exists at least in the ferro-rich case. In comparison with the corresponding Ising model, the Néel phase of this model becomes much narrower in the ferro-rich case, while it is comparable in the antiferro-rich case.

Related papers

Ground-State Phase Diagrams of the Two-Dimensional Quantum Heisenberg Spin Glass Models

Yoshihiko Nonomura, Yukiyasu Ozeki

Ground-state properties of the two-dimensional $S=1/2$ random Heisenberg models are investigated by the exact-diagonalization method. The phase diagram of the bond-random model (the $\pm J$ model) is the same as that of the corresponding Ising spin glass model, in spite of quantum fluctuation. In the site-random model, the spin glass phase exists at least in the ferro-rich case. In comparison with the corresponding Ising model, the Néel phase of this model becomes much narrower in the ferro-rich case, while it is comparable in the antiferro-rich case. KEYWORDS: quantum spin glass, Heisenberg model, ground-state phase transition, site-random model, exact diagonalization

arXiv:cond-mat/9508144•Journal of the Physical Society of Japan•Aug 15, 1995•10 citations

Ground-State Phase Diagram of the Two-Dimensional Quantum Heisenberg Mattis Model

Yoshihiko Nonomura

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. KEYWORDS: quantum spin system, ground state, randomness, Mattis model, Néel order, spin glass order

arXiv:cond-mat/9512144•Journal of the Physical Society of Japan•Feb 15, 1996•2 citations

Ground-State Phase Diagram of the Two-Dimensional Quantum Heisenberg Mattis Model ∗

Yoshihiko Nonomura

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.

•Jan 1, 1995•1 citation

Ground State of Quantum Spin Glass with Infinite Range Interactions

Hidetoshi Nishimori, Y‐h. Taguchi, Takehiko Oguchi

We have investigated the spin-1/2 random Heisenberg model with infinite range interactions by a numerical method. Extrapolation of finite size ( N ≦16) properties to the infinite system has yielded the following results. The average ground state energy is lower than that of the SK model (Ising spin) by about 25%. In the ground state, a critical point between the spin glass and ferromagnetic (mixed) phases exists just around the critical point (\(\tilde{J}_{0}/\tilde{J}{=}1\)) of the corresponding classical random Heisenberg model. Quantum fluctuations are concluded not to change the ground state properties qualitatively.

Journal of the Physical Society of Japan•Feb 15, 1986•5 citations

Two-Dimensional Randomly Frustrated Spin- 1/2 Heisenberg Model

J. Oitmaa, Oleg P. Sushkov

We investigate the properties of S = 1/2 Heisenberg clusters with random frustration using exact diagonalizations. This is a model for a quantum spin glass. We show that the average ground state spin is S proportional to the square root of N, where N is the number of sites. We also calculate the magnetic susceptibility and the spin stiffness and low-energy excitations and discuss these in terms of a semiclassical picture.

arXiv:cond-mat/0105337•Physical Review Letters•Oct 2, 2001•19 citations

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

Yoshihiko Nonomura

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.

Journal of the Physical Society of Japan•Sep 15, 1997•0 citations
Ground-state properties of the two-dimensional S = 1/2 random Heisenberg models are investigated by the exact-diagonalization method. The phase diagram of the bondrandom model (the ±J model) is the same as that of the corresponding Ising spin glass model, in spite of quantum fluctuation. In the site-random model, the spin glass phase exists at least in the ferro-rich case. In comparison with the corresponding Ising model, the Néel phase of this model becomes much narrower in the ferro-rich case, while it is comparable in the antiferro-rich case.
Ground-state properties of the two-dimensional S=1/2S=1/2S=1/2 random Heisenberg models are investigated by the exact-diagonalization method. The phase diagram of the bond-random model (the ±J\pm J±J model) is the same as that of the corresponding Ising spin glass model, in spite of quantum fluctuation. In the site-random model, the spin glass phase exists at least in the ferro-rich case. In comparison with the corresponding Ising model, the Néel phase of this model becomes much narrower in the ferro-rich case, while it is comparable in the antiferro-rich case. KEYWORDS: quantum spin glass, Heisenberg model, ground-state phase transition, site-random model, exact diagonalization
The two-dimensional S=1/2S=1/2S=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. KEYWORDS: quantum spin system, ground state, randomness, Mattis model, Néel order, spin glass order
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.
We have investigated the spin-1/2 random Heisenberg model with infinite range interactions by a numerical method. Extrapolation of finite size ( N ≦16) properties to the infinite system has yielded the following results. The average ground state energy is lower than that of the SK model (Ising spin) by about 25%. In the ground state, a critical point between the spin glass and ferromagnetic (mixed) phases exists just around the critical point (J~0/J~=1\tilde{J}_{0}/\tilde{J}{=}1J~0​/J~=1) of the corresponding classical random Heisenberg model. Quantum fluctuations are concluded not to change the ground state properties qualitatively.
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.