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/0405308 · Physical Review B

Dynamical ac study of the critical behavior in Heisenberg spin glasses

Marco Picco, Félix Ritort

Published Mar 18, 2005• 27 citations
arXivHTMLPDF

Abstract

We present some numerical results for the Heisenberg spin-glass model with Gaussian interactions, in a three-dimensional cubic lattice. We measure the ac susceptibility as a function of temperature and determine an apparent finite temperature transition which is compatible with the chiral-glass temperature transition for this model. The relaxation time diverges like a power law $\ensuremath{\tau}\ensuremath{\sim}{(T\ensuremath{-}{T}_{c})}^{\ensuremath{-}z\ensuremath{\nu}}$ with ${T}_{c}=0.19(4)$ and $z\ensuremath{\nu}=5.0(5)$. Although our data indicate that the spin-glass transition occurs at the same temperature as the chiral glass transition, we cannot exclude the possibility of a chiral-spin coupling scenario for the lowest frequencies investigated.

DOI
10.1103/physrevb.71.100406

Related papers

Dynamical critical phenomena in three-dimensional Heisenberg spin glasses

Mitsuhiro Matsumoto, Koji Hukushima, Hajime Takayama

Spin-glass (SG) and chiral-glass (CG) orderings in three-dimensional (3D) Heisenberg spin glass with and without magnetic anisotropy are studied by using large-scale off-equilibrium Monte Carlo simulations. A characteristic time of relaxation, which diverges at a transition temperature in the thermodynamic limit, is obtained as a function of the temperature and the system size. Based on the finite-size-scaling analysis for the relaxation time, it is found that in the isotropic Heisenberg spin glass, the CG phase transition occurs at a finite temperature, while the SG transition occurs at a lower temperature, which is compatible with zero. Our results of the anisotropic case support the chirality scenario for the phase transitions in the 3D Heisenberg spin glasses.

arXiv:cond-mat/0204225•Physical review. B, Condensed matter•Sep 4, 2002•22 citations

Nonvanishing spin-glass transition temperature of the ±J XY model in three dimensions

Takeo Yamamoto, Takeshi Sugashima, Tota Nakamura

A three-dimensional $\ifmmode\pm\else\textpm\fi{}J$ $XY$ spin-glass model is investigated using the nonequilibrium relaxation method. We have introduced a criterion for the finite-time-scaling analysis. The transition temperature is estimated by a crossing point of the obtained data. The scaling analysis of the relaxation functions of the spin-glass susceptibility and the chiral-glass susceptibility shows that both transitions occur simultaneously. The result is checked by the relaxation functions of the Binder parameters and the glass correlation lengths of the spin and the chirality. All results are consistent if we consider that the transition is driven by the spin degrees of freedom.

arXiv:cond-mat/0403381•Physical Review B•Nov 12, 2004•15 citations

Monte Carlo studies of the spin-chirality decoupling in the three-dimensional Heisenberg spin glass

Takumi Ogawa, Kazuki Uematsu, Hikaru Kawamura

An extensive equilibrium Monte Carlo simulation is performed on the three-dimensional isotropic Heisenberg spin-glass (SG) model with the random nearest-neighbor Gaussian coupling, with particular interest in its chiral-glass (CG) and SG orderings. For this model, the possibility of the spin-chirality decoupling, i.e., the CG order setting in at a higher temperature than that of the SG order, was suggested earlier but still remains controversial. We simulate the model up to the maximum size (linear dimension) $L=48$ under both periodic and open boundary conditions (BCs). In locating the CG and SG transition temperatures ${T}_{\mathrm{CG}}$ and ${T}_{\mathrm{SG}}$ with the $L\ensuremath{\rightarrow}\ensuremath{\infty}$ extrapolation, a variety of independent physical quantities under both BCs are computed and utilized to get larger number of degrees of freedom (NDF). Because of the large NDF up to $\text{NDF}=43$, we succeed in obtaining stable and accurate estimates of the CG and SG transition temperatures, ${T}_{\mathrm{CG}}=0.142\ifmmode\pm\else\textpm\fi{}0.001$ and ${T}_{\mathrm{SG}}=0.{131}_{\ensuremath{-}0.006}^{+0.001}$. No sign of the size crossover is observed. For larger $L$, the CG correlation length progressively outgrows the SG correlation length at low temperatures. These results provide strong numerical support for the spin-chirality decoupling. The critical exponents associated with the CG and SG transitions are evaluated using the finite-size scaling with the scaling correction. For the CG transition, we get the CG exponents, ${\ensuremath{\nu}}_{\mathrm{CG}}=1.36\ifmmode\pm\else\textpm\fi{}0.10$ and ${\ensuremath{\eta}}_{\mathrm{CG}}=0.49\ifmmode\pm\else\textpm\fi{}0.10$, consistent with the corresponding experimental exponents of canonical SG. Implications for the chirality scenario of experimental SG ordering are discussed.

arXiv:1912.02502•Physical review. B./Physical review. B•Jan 22, 2020•11 citations

Nonequilibrium dynamic exponent and spin-glass transitions

Tota Nakamura

Nonequilibrium dynamics of the $\pm J$ Ising, the {\it XY}, and the Heisenberg spin-glass models are investigated in three dimensions. A nonequilibrium dynamic exponent is calculated from the dynamic correlation length. The spin-glass dynamic exponent continuously depends on the temperature. There is no anomaly at the critical temperature as is recently reported by Katzgraber and Campbell. On the other hand, the chiral-glass dynamic exponent takes a constant value above the spin-glass transition temperature ($T_\mathrm{sg}$), and becomes temperature-dependent below $T_\mathrm{sg}$.The finite-time scaling analyses on the spin- and the chiral-glass susceptibility are performed using the temperature dependence of the dynamic exponent. A difference of the spin- and the chiral-glass transition temperatures is resolved in the Heisenberg model. The dynamic critical exponent takes almost the same value for all transitions. It suggests that the spin-glass and the chiral-glass transitions in three dimensions are dynamically universal.

arXiv:cond-mat/0603062•Mar 3, 2006•0 citations

Monte Carlo Studies of the Ordering of the One-Dimensional Heisenberg Spin Glass with Long-Range Power-Law Interactions

Dao Xuan Viet, Hikaru Kawamura

The nature of the ordering of the one-dimensional Heisenberg spin-glass model with a long-range power-law interaction is studied by extensive Monte Carlo simulations, with particular attention to the issue of the spin-chirality decoupling/coupling. Large system sizes up to $L=4096$ are studied. With varying the exponent $σ$ describing the power-law interaction, we observe three distinct types of ordering regimes. For smaller $σ$, the spin and the chirality order at a common finite temperature with a common correlation-length exponent, exhibiting the standard spin-chirality coupling behavior. For intermediate $σ$, the chirality orders at a temperature higher than the spin, exhibiting the spin-chirality decoupling behavior. For larger $σ$, both the spin and the chirality order at zero temperature. We construct a phase diagram in the $σ$ versus the temperature plane, and discuss implications of the results. Critical properties associated with both the chiral-glass and the spin-glass transitions are also determined.

arXiv:1008.2498•Journal of the Physical Society of Japan•Oct 12, 2010•3 citations

Computer simulation of the three-dimensional short-range Heisenberg spin glass

J. A. Olive, A. P. Young, D. Sherrington

The results of large-scale Monte Carlo simulations on a nearest-neighbor Heisenberg spin-glass model are presented. We find that the transition is at zero temperature and that 3 is below the lower critical dimension. Relaxation times follow conventional dynamical scaling and diverge with a power of the temperature T as T\ensuremath{\rightarrow}0.

Physical review. B, Condensed matter•Nov 1, 1986•166 citations
We present some numerical results for the Heisenberg spin-glass model with Gaussian interactions, in a three-dimensional cubic lattice. We measure the ac susceptibility as a function of temperature and determine an apparent finite temperature transition which is compatible with the chiral-glass temperature transition for this model. The relaxation time diverges like a power law \ensuremathτ\ensuremath∼(T\ensuremath−Tc)\ensuremath−z\ensuremathν\ensuremath{\tau}\ensuremath{\sim}{(T\ensuremath{-}{T}_{c})}^{\ensuremath{-}z\ensuremath{\nu}}\ensuremathτ\ensuremath∼(T\ensuremath−Tc​)\ensuremath−z\ensuremathν with Tc=0.19(4){T}_{c}=0.19(4)Tc​=0.19(4) and z\ensuremathν=5.0(5)z\ensuremath{\nu}=5.0(5)z\ensuremathν=5.0(5). Although our data indicate that the spin-glass transition occurs at the same temperature as the chiral glass transition, we cannot exclude the possibility of a chiral-spin coupling scenario for the lowest frequencies investigated.
Spin-glass (SG) and chiral-glass (CG) orderings in three-dimensional (3D) Heisenberg spin glass with and without magnetic anisotropy are studied by using large-scale off-equilibrium Monte Carlo simulations. A characteristic time of relaxation, which diverges at a transition temperature in the thermodynamic limit, is obtained as a function of the temperature and the system size. Based on the finite-size-scaling analysis for the relaxation time, it is found that in the isotropic Heisenberg spin glass, the CG phase transition occurs at a finite temperature, while the SG transition occurs at a lower temperature, which is compatible with zero. Our results of the anisotropic case support the chirality scenario for the phase transitions in the 3D Heisenberg spin glasses.
A three-dimensional $\ifmmode\pm\else\textpm\fi{}J$ XYXYXY spin-glass model is investigated using the nonequilibrium relaxation method. We have introduced a criterion for the finite-time-scaling analysis. The transition temperature is estimated by a crossing point of the obtained data. The scaling analysis of the relaxation functions of the spin-glass susceptibility and the chiral-glass susceptibility shows that both transitions occur simultaneously. The result is checked by the relaxation functions of the Binder parameters and the glass correlation lengths of the spin and the chirality. All results are consistent if we consider that the transition is driven by the spin degrees of freedom.
An extensive equilibrium Monte Carlo simulation is performed on the three-dimensional isotropic Heisenberg spin-glass (SG) model with the random nearest-neighbor Gaussian coupling, with particular interest in its chiral-glass (CG) and SG orderings. For this model, the possibility of the spin-chirality decoupling, i.e., the CG order setting in at a higher temperature than that of the SG order, was suggested earlier but still remains controversial. We simulate the model up to the maximum size (linear dimension) L=48L=48L=48 under both periodic and open boundary conditions (BCs). In locating the CG and SG transition temperatures TCG{T}_{\mathrm{CG}}TCG​ and TSG{T}_{\mathrm{SG}}TSG​ with the $L\ensuremath{\rightarrow}\ensuremath{\infty}$ extrapolation, a variety of independent physical quantities under both BCs are computed and utilized to get larger number of degrees of freedom (NDF). Because of the large NDF up to NDF=43\text{NDF}=43NDF=43, we succeed in obtaining stable and accurate estimates of the CG and SG transition temperatures, ${T}_{\mathrm{CG}}=0.142\ifmmode\pm\else\textpm\fi{}0.001$ and ${T}_{\mathrm{SG}}=0.{131}_{\ensuremath{-}0.006}^{+0.001}$. No sign of the size crossover is observed. For larger LLL, the CG correlation length progressively outgrows the SG correlation length at low temperatures. These results provide strong numerical support for the spin-chirality decoupling. The critical exponents associated with the CG and SG transitions are evaluated using the finite-size scaling with the scaling correction. For the CG transition, we get the CG exponents, ${\ensuremath{\nu}}_{\mathrm{CG}}=1.36\ifmmode\pm\else\textpm\fi{}0.10$ and ${\ensuremath{\eta}}_{\mathrm{CG}}=0.49\ifmmode\pm\else\textpm\fi{}0.10$, consistent with the corresponding experimental exponents of canonical SG. Implications for the chirality scenario of experimental SG ordering are discussed.
Nonequilibrium dynamics of the ±J\pm J±J Ising, the {\it XY}, and the Heisenberg spin-glass models are investigated in three dimensions. A nonequilibrium dynamic exponent is calculated from the dynamic correlation length. The spin-glass dynamic exponent continuously depends on the temperature. There is no anomaly at the critical temperature as is recently reported by Katzgraber and Campbell. On the other hand, the chiral-glass dynamic exponent takes a constant value above the spin-glass transition temperature (TsgT_\mathrm{sg}Tsg​), and becomes temperature-dependent below TsgT_\mathrm{sg}Tsg​.The finite-time scaling analyses on the spin- and the chiral-glass susceptibility are performed using the temperature dependence of the dynamic exponent. A difference of the spin- and the chiral-glass transition temperatures is resolved in the Heisenberg model. The dynamic critical exponent takes almost the same value for all transitions. It suggests that the spin-glass and the chiral-glass transitions in three dimensions are dynamically universal.
The nature of the ordering of the one-dimensional Heisenberg spin-glass model with a long-range power-law interaction is studied by extensive Monte Carlo simulations, with particular attention to the issue of the spin-chirality decoupling/coupling. Large system sizes up to L=4096L=4096L=4096 are studied. With varying the exponent σσσ describing the power-law interaction, we observe three distinct types of ordering regimes. For smaller σσσ, the spin and the chirality order at a common finite temperature with a common correlation-length exponent, exhibiting the standard spin-chirality coupling behavior. For intermediate σσσ, the chirality orders at a temperature higher than the spin, exhibiting the spin-chirality decoupling behavior. For larger σσσ, both the spin and the chirality order at zero temperature. We construct a phase diagram in the σσσ versus the temperature plane, and discuss implications of the results. Critical properties associated with both the chiral-glass and the spin-glass transitions are also determined.