Short-range Spin Glasses Research Articles

Equilibrium and Non-Equilibrium Dynamics of Short-Range Spin-Glasses

A recently developed theoretical description of the statics and dynamics of short-range spin glasses is summarized. The main features can be described in terms of droplet excitations and the dynamics of domain walls. Predictions for equilibrium properties, the global structure of the phase diagram, and non-equilibrium dynamic effects are briefly discussed.

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

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.

Theory of the spin-glass state on a spin-density-wave host

The spin-spin interaction in the itinerant-electron antiferromagnet has been calculated. The short range character of this interaction gives rise to the short-range spin glass. The thermodynamics of this state has been analysed in the low and high temperature domains. The specific behaviour of this state compared with the Abrikosov theory showed the importance of the non-oscillatory contribution from the spin-spin interaction.

Metastable states, domain walls, domain-flip transitions, and inhomogeneous ordering in the short-range Ising spin glass.

A mean-field study of the short-range Ising spin glass suggests a cascade (perhaps a continuum in the thermodynamic limit) of non- thermodynamic first-order transitions (domain flips) in the ordered state. The metastable states are domain states and have a tree structure.

Anderson clusters and inhomogeneous ordering in the short-range Ising spin glass.

In naive mean-field theory, the initial ordering in the short-range Ising spin glass is in the form of internally inhomogeneous clusters which form in regions with favorable bond configurations. These ``Anderson clusters'' are identified with the clusters inferred from experiments. The metastable states are domain states and have a tree structure, despite violation of the ultrametricity condition obtained in the infinite-range version of the model.

Dynamics of three-dimensional Ising spin glasses in thermal equilibrium.

I present an analysis of the dynamic behavior of short-range Ising spin glasses observed in stochastic simulations. The time dependence of the order parameter q(t)=〈${S}_{x}$(0)${S}_{x}$(t)〉\ifmmode\bar\else\textasciimacron\fi{}---which is the same as that of the structure factor---and the time dependence of the related dynamic correlation functions have been recorded with good statistics and very long observation times. The spin-glass model with a symmetric distribution of discrete nearest-neighbor \ifmmode\pm\else\textpm\fi{}J interactions on a simple-cubic lattice was used. Simulations were performed with a special fast computer, allowing for the first-time investigation of the equilibrium dynamics for a wide range of temperatures (0.7\ensuremath{\le}kT/J\ensuremath{\le}5.0) and lattice sizes (${8}^{3}$, ${16}^{3}$, ${32}^{3}$, and ${64}^{3}$). I have found that the empirical formula q(t)=${\mathrm{ct}}^{\mathrm{\ensuremath{-}}x}$exp(-\ensuremath{\omega}${t}^{\ensuremath{\beta}}$) with temperature-dependent exponents x(T) and \ensuremath{\beta}(T) describes the decay very well at all temperatures above the spin-glass transition. In the spin-glass phase, only the algebraic decay q(t)=${\mathrm{ct}}^{\mathrm{\ensuremath{-}}x}$ could be observed, with different temperature dependences of the exponent x(T). The dynamic scaling hypothesis and finite-size scaling explain well the observed temperature and size dependence of the data, and the functional form of the correlation functions is com- patible with the scaling form if corrections to scaling are taken into account. The scaling behavior and the dynamic and static critical exponents found in my simulations are in reasonable agreement with recent experiments performed on insulating spin glasses, showing that despite its simplicity the discrete model of spin glasses analyzed in this work displays behavior similar to that seen in nature.

Fluctuation-driven first-order transition in the short-range Potts spin glass.

Fluctuation-driven first-order transition in the short-range Potts spin glass.

Dimensional reduction in entropy dominated transitions with possible application to short-range spin-glasses

The author studies from general considerations, the critical behaviour of systems which condense, at their critical temperature Tc, into a weakly coherent critical state with an infinitely large number of weakly coherent critical state with an infinitely large number of internal degrees of freedom. If this number (per volume of size xi d where xi is the correlation length) varies as xi rho with 0< rho <d, the reduced dimension d=d- rho is naturally associated with the extremely large fluctuations at the transition. Assuming that xi approximately (T-Tc)- nu with nu = nu (d) of some regular d-dimensional model, the negative value of the specific-heat exponents alpha = alpha (d)- rho nu follows. He proposes a relation between rho and other critical exponents and compute self-consistently the dimensional reduction. The short-range Ising spin glass below an intermediate critical dimensionality (probably dicd=4) may provide a realisation of such an entropy-dominated transition. If all frustration effects are accounted for by the effective shift in dimensionality, the following consequences are anticipated: (i) The lower critical dimension is dlcd=2. (ii) The 3d exponents are nu SG=1 and alpha SG=-1. These conjectures agree surprisingly well with several recent numerical simulations.

Monte Carlo studies of short-range Ising spin glasses in zero field

Results are presented of Monte Carlo simulations for a three-dimensional nearest-neighbour Ising spin glass model with a '+/-J' distribution of interactions on a simple cubic lattice. The data for the spin glass susceptibility, the correlation length and the logarithm of an 'average' relaxation time are consistent with a transition at T=0. However, a similarly good fit is also obtained with a finite transition temperature, Tc, if Tc<or approximately=1 (in units of J). In addition, earlier data on the corresponding two-dimensional model are re-analysed.

Short-range Ising spin glasses

In the framework of the replica method, spatial fluctuations in short-range Ising spin glasses are studied by use of the gaussian approximation.

Residual magnetic entropy and metastable states of the Edwards-Anderson Ising spin glass

The residual magnetic entropy is calculated for the short-range Edwards-Anderson spin-glass model by the Monte Carlo method. For slow cooling, a finite value of the residual magnetic entropy is obtained, which depends only weakly on the cooling rate. A comparison with available information about the total density of states and the density of metastable states suggests that the residual magnetic entropy is determined by the density of metastable states at the residual energy of the spin glass at zero temperature.