Spin-glass and chiral-glass orderings of a three-dimensional isotropic Heisenberg spin glass are studied both by equilibrium and off-equilibrium Monte Carlo simulations with emphasis on their dynamical aspects. The model is found to exhibit a finite-temperature chiral-glass transition without the conventional spin-glass order. Although chirality is an Ising-like quantity from symmetry, universality class of the chiral-glass transition appears to be different from that of the standard Ising spin glass. In the off-equilibrium simulation, while the spin autocorrelation exhibits only an interrupted aging, the chirality autocorrelation persists to exhibit a pronounced aging effect reminiscent of the one observered in the mean-field model.Spin-glass and chiral-glass orderings of a three-dimensional isotropic Heisenberg spin glass are studied both by equilibrium and off-equilibrium Monte Carlo simulations with emphasis on their dynamical aspects. The model is found to exhibit a finite-temperature chiral-glass transition without the conventional spin-glass order. Although chirality is an Ising-like quantity from symmetry, universality class of the chiral-glass transition appears to be different from that of the standard Ising spin glass. In the off-equilibrium simulation, while the spin autocorrelation exhibits only an interrupted aging, the chirality autocorrelation persists to exhibit a pronounced aging effect reminiscent of the one observered in the mean-field model.

International Journal of Modern Physics CDec 1, 19994 citations

Dynamical Simulation of Spin-Glass and Chiral-Glass Orderings in Three-Dimensional Heisenberg Spin Glasses

Hikaru Kawamura

Spin-glass and chiral-glass orderings in three-dimensional Heisenberg spin glasses are studied with and without random magnetic anisotropy by dynamical Monte Carlo simulations. In the isotropic case, clear evidence of a finite-temperature chiral-glass transition is presented. While the spin autocorrelation exhibits only an interrupted aging, the chirality autocorrelation persists to exhibit a pronounced aging effect reminiscent of the one observed in the mean-field model. In the anisotropic case, asymptotic mixing of the spin and the chirality is observed in the off-equilibrium dynamics.Spin-glass and chiral-glass orderings in three-dimensional Heisenberg spin glasses are studied with and without random magnetic anisotropy by dynamical Monte Carlo simulations. In the isotropic case, clear evidence of a finite-temperature chiral-glass transition is presented. While the spin autocorrelation exhibits only an interrupted aging, the chirality autocorrelation persists to exhibit a pronounced aging effect reminiscent of the one observed in the mean-field model. In the anisotropic case, asymptotic mixing of the spin and the chirality is observed in the off-equilibrium dynamics.

arXiv:cond-mat/9805117Physical Review LettersJun 15, 199874 citations

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.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/0204225Physical review. B, Condensed matterSep 4, 200222 citations

Phase Transition of a Heisenberg Spin-Glass Model in Three Dimensions

Fumitaka Matsubara, Takayuki Shirakura, Shin-ichi Endoh

We study the phase transition of the $\pm J$ Heisenberg model in three dimensions. Using a dynamical simulation method that removes a drift of the system, the existence of the spin-glass (SG) phase at low temperatures is suggested. The transition temperature is estimated to be $T_{\rm SG} \sim 0.18J$ from both equilibrium and off-equilibrium Monte-Carlo simulations. Our result contradicts the chirality mechanism of the phase transition reported recently by Kawamura which claims that it is not the spins but the chiralities of the spins that are ordered in Heisenberg SG systems.We study the phase transition of the $\pm J$ Heisenberg model in three dimensions. Using a dynamical simulation method that removes a drift of the system, the existence of the spin-glass (SG) phase at low temperatures is suggested. The transition temperature is estimated to be $T_{\rm SG} \sim 0.18J$ from both equilibrium and off-equilibrium Monte-Carlo simulations. Our result contradicts the chirality mechanism of the phase transition reported recently by Kawamura which claims that it is not the spins but the chiralities of the spins that are ordered in Heisenberg SG systems.

arXiv:cond-mat/0011218Nov 13, 20000 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.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:1912.02502Physical review. B./Physical review. BJan 22, 202011 citations

Monte Carlo simulations of the three-dimensional XY spin glass focusing on chiral and spin order

Tomoyuki Obuchi, Hikaru Kawamura

The ordering of the three-dimensional isotropic $\mathit{XY}$ spin glass with nearest-neighbor random Gaussian coupling is studied by extensive Monte Carlo simulations. To investigate the ordering of the spin and the chirality, we compute several independent physical quantities including the glass order parameter, the Binder parameter, the correlation-length ratio, the overlap distribution, and the non-self-averageness parameter, etc., for both the spin-glass (SG) and the chiral-glass (CG) degrees of freedom. Evidence of spin-chirality decoupling, i.e., that the CG and SG order occur at two separate temperatures, $0<{T}_{\mathrm{SG}}<{T}_{\mathrm{CG}}$ , is obtained from the glass order parameter, and is fully corroborated by the Binder parameter. By contrast, the CG correlation-length ratio yields a rather pathological and inconsistent result in the range of sizes we studied, which may originate from the finite-size effect associated with a significant short-length dropoff of the spatial CG correlations. Finite-size-scaling analysis yields the CG exponents ${\ensuremath{\nu}}_{\mathrm{CG}}=1.{36}_{\ensuremath{-}0.37}^{+0.15}$ and ${\ensuremath{\eta}}_{\mathrm{CG}}=0.{26}_{\ensuremath{-}0.26}^{+0.29}$, and the SG exponents ${\ensuremath{\nu}}_{\mathrm{SG}}=1.{22}_{\ensuremath{-}0.06}^{+0.26}$ and ${\ensuremath{\eta}}_{\mathrm{SG}}=\ensuremath{-}0.{54}_{\ensuremath{-}0.52}^{+0.24}$. The exponents obtained are close to those of the Heisenberg SG, but are very different from those of the Ising SG. The chiral overlap distribution and the chiral Binder parameter exhibit the feature of a continuous one-step replica-symmetry breaking (1RSB), consistently with previous reports. Such a 1RSB feature is again like that of the Heisenberg SG, but is different from the Ising SG, which may be the cause of the difference in the CG critical properties from those of the Ising SG despite the common ${Z}_{2}$ symmetry.The ordering of the three-dimensional isotropic $\mathit{XY}$ spin glass with nearest-neighbor random Gaussian coupling is studied by extensive Monte Carlo simulations. To investigate the ordering of the spin and the chirality, we compute several independent physical quantities including the glass order parameter, the Binder parameter, the correlation-length ratio, the overlap distribution, and the non-self-averageness parameter, etc., for both the spin-glass (SG) and the chiral-glass (CG) degrees of freedom. Evidence of spin-chirality decoupling, i.e., that the CG and SG order occur at two separate temperatures, $0<{T}_{\mathrm{SG}}<{T}_{\mathrm{CG}}$, is obtained from the glass order parameter, and is fully corroborated by the Binder parameter. By contrast, the CG correlation-length ratio yields a rather pathological and inconsistent result in the range of sizes we studied, which may originate from the finite-size effect associated with a significant short-length dropoff of the spatial CG correlations. Finite-size-scaling analysis yields the CG exponents ${\ensuremath{\nu}}_{\mathrm{CG}}=1.{36}_{\ensuremath{-}0.37}^{+0.15}$ and ${\ensuremath{\eta}}_{\mathrm{CG}}=0.{26}_{\ensuremath{-}0.26}^{+0.29}$, and the SG exponents ${\ensuremath{\nu}}_{\mathrm{SG}}=1.{22}_{\ensuremath{-}0.06}^{+0.26}$ and ${\ensuremath{\eta}}_{\mathrm{SG}}=\ensuremath{-}0.{54}_{\ensuremath{-}0.52}^{+0.24}$. The exponents obtained are close to those of the Heisenberg SG, but are very different from those of the Ising SG. The chiral overlap distribution and the chiral Binder parameter exhibit the feature of a continuous one-step replica-symmetry breaking (1RSB), consistently with previous reports. Such a 1RSB feature is again like that of the Heisenberg SG, but is different from the Ising SG, which may be the cause of the difference in the CG critical properties from those of the Ising SG despite the common ${Z}_{2}$ symmetry.

arXiv:1212.3804Physical Review BMay 31, 201312 citations

We study the phase transition of the

\pm J

Heisenberg model in three dimensions. Using a dynamical simulation method that removes a drift of the system, the existence of the spin-glass (SG) phase at low temperatures is suggested. The transition temperature is estimated to be

T_{\rm SG} \sim 0.18J

from both equilibrium and off-equilibrium Monte-Carlo simulations. Our result contradicts the chirality mechanism of the phase transition reported recently by Kawamura which claims that it is not the spins but the chiralities of the spins that are ordered in Heisenberg SG systems.

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.

The ordering of the three-dimensional isotropic

\mathit{XY}

spin glass with nearest-neighbor random Gaussian coupling is studied by extensive Monte Carlo simulations. To investigate the ordering of the spin and the chirality, we compute several independent physical quantities including the glass order parameter, the Binder parameter, the correlation-length ratio, the overlap distribution, and the non-self-averageness parameter, etc., for both the spin-glass (SG) and the chiral-glass (CG) degrees of freedom. Evidence of spin-chirality decoupling, i.e., that the CG and SG order occur at two separate temperatures,

0<{T}_{\mathrm{SG}}<{T}_{\mathrm{CG}}

, is obtained from the glass order parameter, and is fully corroborated by the Binder parameter. By contrast, the CG correlation-length ratio yields a rather pathological and inconsistent result in the range of sizes we studied, which may originate from the finite-size effect associated with a significant short-length dropoff of the spatial CG correlations. Finite-size-scaling analysis yields the CG exponents ${\ensuremath{\nu}}_{\mathrm{CG}}=1.{36}_{\ensuremath{-}0.37}^{+0.15}$ and ${\ensuremath{\eta}}_{\mathrm{CG}}=0.{26}_{\ensuremath{-}0.26}^{+0.29}$, and the SG exponents ${\ensuremath{\nu}}_{\mathrm{SG}}=1.{22}_{\ensuremath{-}0.06}^{+0.26}$ and ${\ensuremath{\eta}}_{\mathrm{SG}}=\ensuremath{-}0.{54}_{\ensuremath{-}0.52}^{+0.24}$. The exponents obtained are close to those of the Heisenberg SG, but are very different from those of the Ising SG. The chiral overlap distribution and the chiral Binder parameter exhibit the feature of a continuous one-step replica-symmetry breaking (1RSB), consistently with previous reports. Such a 1RSB feature is again like that of the Heisenberg SG, but is different from the Ising SG, which may be the cause of the difference in the CG critical properties from those of the Ising SG despite the common

{Z}_{2}

symmetry.