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

arXiv:cond-mat/9707059 · Physical Review Letters

Low Temperature Phase of Asymmetric Spin Glass Model in Two Dimensions

Takayuki Shirakura, Fumitaka Matsubara

Published Oct 13, 1997• 23 citations
arXivHTMLPDF

Abstract

We investigate low temperature properties of a random Ising model with $+J$ and $\ensuremath{-}aJ$ $(a\ensuremath{\ne}1)$ bonds in two dimensions using a cluster heat bath method. It is found that the Binder parameters ${g}_{L}$ for different sizes of the lattice come together at almost the same temperature, implying the occurrence of the spin glass (SG) phase transition. From results of finite size scaling analyses, we suggest that the SG phase really occurs at low temperatures, which is characterized by a power law decay of spin correlations.

DOI
10.1103/physrevlett.79.2887

Related papers

Evidence of a Spin-Glass Phase Transition ofa Site-Random Ising Model in Two Dimensions

Takayuki Shirakura, Fumitaka Matsubara

We study a site-random Ising (SRI) model in two dimensions (2D) using a Monte Carlo method. It is found that the Binder parameter g L 's for different sizes of the lattice L come together at almost the same temperature as in the ± J model in 3D. Finite-size scaling analyses give results which are compatible with the assumption of a finite, nonzero transition temperature ( T c ≠0), although the scaling temperature range is not large. We suggest that in the SRI model a spin glass (SG) phase transition occurs at T c ≠0 even in 2D.

Journal of the Physical Society of Japan•Jul 15, 1995•11 citations

Phase Transition of Ising Spin Glass Models in Two Dimensions

Michinori Shiomi, Fumitaka Matsubara, Takayuki Shirakura

We examine the phase transition of Ising spin glass models in two dimensions (2D), calculating complementary two quantities, i.e., the interface free energy \(\overline{\Delta F(T)}\) and the Binder parameter g L , on finite L × L ( L ≤24) lattices at very low temperatures T . We find that these quantities exhibit quite different features depending on the distribution of bonds. For the ± J distribution, \(\overline{\Delta F(T)}\) at very low temperatures slightly increases with L and g L intersect at T ∼0.25 J . These results suggest a non-zero temperature phase transition, T c ≠0. On the other hand, for the Gaussian distribution, \(\overline{\Delta F(T)}\) decreases as L increases even at T = 0 and g L for different L converges to unity at T = 0. These results confirm the assumption of the zero temperature phase transition, T c = 0. Finite-size scaling analyses support those results. Thus we suggest that, in 2D, the existence of a finite-temperature phase transition depends on the distribution of bonds and it exists when the bond distribution is ± J .

Journal of the Physical Society of Japan•Sep 1, 2000•10 citations

Reexamination of the SG Transition in the Two-Dimensional ±JIsing Model

Takayuki Shirakura, Fumitaka Matsubara

Using the exchange Monte Carlo method, we reexamine the ± J Ising spin glass (SG) transition in two dimensions. We calculate the SG susceptibility, the Binder cumulant and the distribution function of spin overlap at low temperatures. In contrast to our expectations, better finite-size scaling plots are obtained for a finite, nonzero transition temperature than for a zero transition temperature.

Journal of the Physical Society of Japan•Oct 15, 1996•16 citations

Phase Transition of Three-Dimensional Site-Random Ising Model with Short-Range Interactions

Takayuki Shirakura, Fumitaka Matsubara

We study a short-range site-random Ising model in three dimensions (3D) using a Monte Carlo (MC) method and find a phase transition to a spin glass (SG) phase at a very high temperature ( T c ≃2.83 J). Values of the critical exponents estimated from a finite-size scaling analysis are different from those in both the 3D\(\mp J\) Ising model and the 3D Ising ferromagnet. We suggest that the SG phase in this model is a new SG phase which is characterized by a nonzero SG order parameter q ≠0.

Journal of the Physical Society of Japan•Sep 15, 1993•9 citations

Three-dimensional Heisenberg spin-glass models with and without random anisotropy

F Matsubara, T Shirakura, S Endoh +1 more

We re-examine the spin-glass (SG) phase transition of the ± J Heisenberg models with and without random anisotropy D in three dimensions ( d = 3) using two complementary methods, i.e., (i) the defect energy method and (ii) the Monte Carlo method. We reveal that the conventional defect energy method is not convincing and propose a new method which considers the stiffness of the lattice itself. Using the method, we show that the stiffness exponent θ has a positive value (θ > 0) even when D = 0. Considering the stiffness at finite temperatures, we obtain the SG phase transition temperature of T SG ∼ 0.19 J for D = 0. On the other hand, a large scale MC simulation shows that, in contrast to the previous results, a scaling plot of the SG susceptibility χ SG for D = 0 is obtained using almost the same transition temperature of T SG ∼ 0.18 J . Hence we believe that the SG phase transition occurs in the Heisenberg SG model in d = 3.

arXiv:cond-mat/0309573•Journal of Physics A Mathematical and General•Oct 15, 2003•15 citations

Spin glass phase in random-bond Ising model

Luecha Tungchanachaianun, Chatchai Srinitiwarawong

The phase diagram of modified random-bond Ising model has been investigated. The model is based on random-bond Ising model in which the distribution of magnetic interaction is Gaussian rather than the uniform distribution. The center of the distribution is positive so that most of the interactions are ferromagnetic. However the width of the distribution can be varied. The increasing of the width (J) induces disorder to this system. It is expected that when the tail of the distribution reaches the negative interaction region, the system at low temperature shows the cross over between ferromagnetic phase and spin glass phase. By using magnetization and spin glass magnetization, three ordered phases appear in the J-T phase diagram: (1) the ferromagnetic (FM) phase; (2) the spin glass (SG) phase; (3) the paramagnetic (PM) phase. At very high temperature the system is in paramagnetic phase. At low temperature and small distribution the system is in ferromagnetic phase. The cross over between ferromagnetic phase and spin glass phase is visible as the width of the interaction distribution is increase at low temperature. The critical temperature has been obtained by using Binder cumulant of spin glass magnetization.

•Jan 1, 2009•0 citations
We investigate low temperature properties of a random Ising model with +J+J+J and \ensuremath−aJ\ensuremath{-}aJ\ensuremath−aJ (a\ensuremath≠1)(a\ensuremath{\ne}1)(a\ensuremath=1) bonds in two dimensions using a cluster heat bath method. It is found that the Binder parameters gL{g}_{L}gL​ for different sizes of the lattice come together at almost the same temperature, implying the occurrence of the spin glass (SG) phase transition. From results of finite size scaling analyses, we suggest that the SG phase really occurs at low temperatures, which is characterized by a power law decay of spin correlations.
We study a site-random Ising (SRI) model in two dimensions (2D) using a Monte Carlo method. It is found that the Binder parameter g L 's for different sizes of the lattice L come together at almost the same temperature as in the ± J model in 3D. Finite-size scaling analyses give results which are compatible with the assumption of a finite, nonzero transition temperature ( T c ≠0), although the scaling temperature range is not large. We suggest that in the SRI model a spin glass (SG) phase transition occurs at T c ≠0 even in 2D.
We examine the phase transition of Ising spin glass models in two dimensions (2D), calculating complementary two quantities, i.e., the interface free energy ΔF(T)‾\overline{\Delta F(T)}ΔF(T)​ and the Binder parameter g L , on finite L × L ( L ≤24) lattices at very low temperatures T . We find that these quantities exhibit quite different features depending on the distribution of bonds. For the ± J distribution, ΔF(T)‾\overline{\Delta F(T)}ΔF(T)​ at very low temperatures slightly increases with L and g L intersect at T ∼0.25 J . These results suggest a non-zero temperature phase transition, T c ≠0. On the other hand, for the Gaussian distribution, ΔF(T)‾\overline{\Delta F(T)}ΔF(T)​ decreases as L increases even at T = 0 and g L for different L converges to unity at T = 0. These results confirm the assumption of the zero temperature phase transition, T c = 0. Finite-size scaling analyses support those results. Thus we suggest that, in 2D, the existence of a finite-temperature phase transition depends on the distribution of bonds and it exists when the bond distribution is ± J .
We study a short-range site-random Ising model in three dimensions (3D) using a Monte Carlo (MC) method and find a phase transition to a spin glass (SG) phase at a very high temperature ( T c ≃2.83 J). Values of the critical exponents estimated from a finite-size scaling analysis are different from those in both the 3D∓J\mp J∓J Ising model and the 3D Ising ferromagnet. We suggest that the SG phase in this model is a new SG phase which is characterized by a nonzero SG order parameter q ≠0.
We re-examine the spin-glass (SG) phase transition of the ± J Heisenberg models with and without random anisotropy D in three dimensions ( d = 3) using two complementary methods, i.e., (i) the defect energy method and (ii) the Monte Carlo method. We reveal that the conventional defect energy method is not convincing and propose a new method which considers the stiffness of the lattice itself. Using the method, we show that the stiffness exponent θ has a positive value (θ > 0) even when D = 0. Considering the stiffness at finite temperatures, we obtain the SG phase transition temperature of T SG ∼ 0.19 J for D = 0. On the other hand, a large scale MC simulation shows that, in contrast to the previous results, a scaling plot of the SG susceptibility χ SG for D = 0 is obtained using almost the same transition temperature of T SG ∼ 0.18 J . Hence we believe that the SG phase transition occurs in the Heisenberg SG model in d = 3.
The phase diagram of modified random-bond Ising model has been investigated. The model is based on random-bond Ising model in which the distribution of magnetic interaction is Gaussian rather than the uniform distribution. The center of the distribution is positive so that most of the interactions are ferromagnetic. However the width of the distribution can be varied. The increasing of the width (J) induces disorder to this system. It is expected that when the tail of the distribution reaches the negative interaction region, the system at low temperature shows the cross over between ferromagnetic phase and spin glass phase. By using magnetization and spin glass magnetization, three ordered phases appear in the J-T phase diagram: (1) the ferromagnetic (FM) phase; (2) the spin glass (SG) phase; (3) the paramagnetic (PM) phase. At very high temperature the system is in paramagnetic phase. At low temperature and small distribution the system is in ferromagnetic phase. The cross over between ferromagnetic phase and spin glass phase is visible as the width of the interaction distribution is increase at low temperature. The critical temperature has been obtained by using Binder cumulant of spin glass magnetization.