Dynamical aspects of a three-dimensional Heisenberg spin glass (original) (raw)
Related papers
Chiral-glass transition and replica symmetry breaking of a three-dimensional heisenberg spin glass
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 2000
Extensive equilibrium Monte Carlo simulations are performed for a three-dimensional Heisenberg spin glass with the nearest-neighbor Gaussian coupling to investigate its spin-glass and chiral-glass orderings. The occurrence of a finite-temperature chiral-glass transition without the conventional spin-glass order is established. Critical exponents characterizing the transition are different from those of the standard Ising spin glass. The calculated overlap distribution suggests the appearance of a peculiar type of replica-symmetry breaking in the chiral-glass ordered state.
Journal of the Physical Society of Japan, 2010
The nature of the ordering of the one-dimensional Heisenberg spin-glass model with a longrange 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.
Finite temperature phase transition in the three-dimensional Heisenberg ±J spin glass model
Journal of Applied Physics, 2007
The three-dimensional Heisenberg spin glass model with ±J interactions is studied using an over-relaxed Monte Carlo algorithm. We have measured the correlation length , and using the crossing of / L for different L find a finite temperature spin glass transition, with T SG = 0.220͑5͒. In addition, we have varied the number of Monte Carlo steps used prior to, and during, thermal averaging to control the effects of finite time averaging. We find that the over-relaxation algorithm allows for an accurate measurements using as few as 300 Monte Carlo steps.
Coexistence of spin-glass and ferromagnetic order in the ±J Heisenberg spin-glass model
Physical Review B, 2007
simulations of the bond-frustrated ±J Heisenberg model confirm the existence of a finite temperature spin-glass transition at T SG = 0.220͑5͒. Remarkably, this transition temperature is composition dependent, rising to T SG = 0.25͑1͒ by the ferromagnet-spin-glass boundary. Coexistence of ferromagnetic and spin-glass ordering is observed at low frustration levels for T Ͻ T xy , and the composition dependence of this transition is also followed. The behavior we observe below T xy agrees with both the mean field prediction and the experimental observations while being inconsistent with "re-entrance," which demands a loss of ferromagnetic order. The complete phase diagram is presented.
Critical aspects of three-dimensional anisotropic spin-glass models
The European Physical Journal B, 2015
We study the ±J three-dimensional Ising model with a longitudinal anisotropic bond randomness on the simple cubic lattice. The random exchange interaction is applied only in the z direction, whereas in the other two directions, xy -planes, we consider ferromagnetic exchange. By implementing an effective parallel tempering scheme, we outline the phase diagram of the model and compare it to the corresponding isotropic one, as well as to a previously studied anisotropic (transverse) case. We present a detailed finite-size scaling analysis of the ferromagnetic -paramagnetic and spin glass -paramagnetic transition lines, and we also discuss the ferromagnetic -spin glass transition regime. We conclude that the present model shares the same universality classes with the isotropic model, but at the symmetric point has a considerably higher transition temperature from the spin-glass state to the paramagnetic phase. Our data for the ferromagnetic -spin glass transition line are supporting a forward behavior in contrast to the reentrant behavior of the isotropic model.
Spin glasses without time-reversal symmetry and the absence of a genuine structural glass transition
Physical Review E, 2000
We study the three-spin model and the Ising spin glass in a field using Migdal-Kadanoff approximation. The flows of the couplings and fields indicate no phase transition, but they show even for the three-spin model a slow crossover to the asymptotic high-temperature behaviour for strong values of the couplings. We also evaluated a quantity that is a measure of the degree of non-self-averaging, and we found that it can become large for certain ranges of the parameters and the system sizes. For the spin glass in a field the maximum of non-self-averaging follows for given system size a line that resembles the de Almeida-Thouless line. We conclude that non-self-averaging found in Monte-Carlo simulations cannot be taken as evidence for the existence of a low-temperature phase with replica-symmetry breaking. Models similar to the three-spin model have been extensively discussed in order to provide a description of structural glasses. Their theory at mean-field level resembles the mode-coupling theory of real glasses. At that level the one-step replica symmetry approach breaking predicts two transitions, the first transition being dynamical and the second thermodynamical. Our results suggest that in real finite dimensional glasses there will be no genuine transitions at all, but that some features of mean-field theory could still provide some useful insights.
Dynamical ac study of the critical behavior in Heisenberg spin glasses
Physical Review B, 2005
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 τ ∼ (T − T c) −zν with T c = 0.19(4) and zν = 5.0(5). Although our data indicates 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.
Numerical Study of Spin and Chiral Order in a Two-Dimensional XY Spin Glass
Physical Review Letters, 1999
The two dimensional XY spin glass in is studied numerically by a finite size defect energy scaling method at T = 0 in the vortex representation which allows us to compute the exact (in principle) spin and chiral domain wall energies. We confirm earlier predictions that there is no glass phase at any finite T . Our results strongly support the conjecture that both spin and chiral order have the same correlation length exponent νs = νc ≈ 2.70. Preliminary results in 3d are also obtained.
Evidence for the double degeneracy of the ground state in the three-dimensional ± J spin glass
Physical Review B, 2002
A bivariate version of the multicanonical Monte Carlo method and its application to the simulation of the three-dimensional ±J Ising spin glass are described. We found the autocorrelation time associated with this particular multicanonical method was approximately proportional to the system volume, which is a great improvement over previous methods applied to spin-glass simulations.