Equilibrium valleys in spin glasses at low temperature

We investigate the 3-dimensional Edwards-Anderson spin glass model at low temperature on simple cubic lattices of sizes up to L=12. Our findings show a strong continuity among T>0 physical features and those found previously at T=0, leading to a scenario with emerging mean field like characteristics that are enhanced in the large volume limit. For instance, the picture of space filling sponges seems to survive in the large volume limit at T>0, while entropic effects play a crucial role in determining the free-energy degeneracy of our finite volume states. All of our analysis is applied to equilibrium configurations obtained by a parallel tempering on 512 different disorder realizations. First, we consider the spatial properties of the sites where pairs of independent spin configurations differ and we introduce a modified spin overlap distribution which exhibits a non-trivial limit for large L. Second, after removing the Z_2 (+-1) symmetry, we cluster spin configurations into valleys. On average these valleys have free-energy differences of O(1), but a difference in the (extensive) internal energy that grows significantly with L; there is thus a large interplay between energy and entropy fluctuations. We also find that valleys typically differ by sponge-like space filling clusters, just as found previously for low-energy system-size excitations above the ground state.Comment: 10 pages, 8 figures, RevTeX format. Clarifications and additional reference

The ground state energy of the Edwards-Anderson spin glass model with a parallel tempering Monte Carlo algorithm

We study the efficiency of parallel tempering Monte Carlo technique for calculating true ground states of the Edwards-Anderson spin glass model. Bimodal and Gaussian bond distributions were considered in two and three-dimensional lattices. By a systematic analysis we find a simple formula to estimate the values of the parameters needed in the algorithm to find the GS with a fixed average probability. We also study the performance of the algorithm for single samples, quantifying the difference between samples where the GS is hard, or easy, to find. The GS energies we obtain are in good agreement with the values found in the literature. Our results show that the performance of the parallel tempering technique is comparable to more powerful heuristics developed to find the ground state of Ising spin glass systems.Comment: 30 pages, 17 figures. A new section added. Accepted for publication in Physica

Spin glass transition in a magnetic field: a renormalization group study

We study the transition of short range Ising spin glasses in a magnetic field, within a general replica symmetric field theory, which contains three masses and eight cubic couplings, that is defined in terms of the fields representing the replicon, anomalous and longitudinal modes. We discuss the symmetry of the theory in the limit of replica number n to 0, and consider the regular case where the longitudinal and anomalous masses remain degenerate. The spin glass transitions in zero and non-zero field are analyzed in a common framework. The mean field treatment shows the usual results, that is a transition in zero field, where all the modes become critical, and a transition in non-zero field, at the de Almeida-Thouless (AT) line, with only the replicon mode critical. Renormalization group methods are used to study the critical behavior, to order epsilon = 6-d. In the general theory we find a stable fixed-point associated to the spin glass transition in zero field. This fixed-point becomes unstable in the presence of a small magnetic field, and we calculate crossover exponents, which we relate to zero-field critical exponents. In a finite magnetic field, we find no physical stable fixed-point to describe the AT transition, in agreement with previous results of other authors.Comment: 36 pages with 4 tables. To be published in Phys. Rev.

Novel order parameter to describe the critical behavior of Ising spin glass models

A novel order parameter $\Phi$ for spin glasses is defined based on topological criteria and with a clear physical interpretation. $\Phi$ is first investigated for well known magnetic systems and then applied to the Edwards-Anderson $\pm J$ model on a square lattice, comparing its properties with the usual $q$ order parameter. Finite size scaling procedures are performed. Results and analyses based on $\Phi$ confirm a zero temperature phase transition and allow to identify the low temperature phase. The advantages of $\Phi$ are brought out and its physical meaning is established.Comment: 13 pages, 4 figures, to appear in Physica

Dynamic scaling and aging phenomena in short-range Ising spin glass: Cu0.5_{0.5}Co0.5_{0.5}Cl2_{2}-FeCl3_{3} graphite bi-intercalation compound

Static and dynamic behavior of short-range Ising-spin glass Cu$_{0.5}$Co$_{0.5}$Cl$_{2}$-FeCl$_{3}$ graphite bi-intercalation compounds (GBIC) has been studied with SQUID DC and AC magnetic susceptibility. The $T$ dependence of the zero-field relaxation time $\tau$ above a spin-freezing temperature $T_{g}$ (= 3.92 $\pm$ 0.11 K) is well described by critical slowing down. The absorption $\chi^{\prime\prime}$ below $T_{g}$ decreases with increasing angular frequency $\omega$, which is in contrast to the case of 3D Ising spin glass. The dynamic freezing temperature $T_{f}(H,\omega)$ at which d$M_{FC}(T,H)/$d$H=\chi^{\prime}(T,H=0,\omega)$, is determined as a function of frequency (0.01 Hz $\leq \omega/2\pi \leq$ 1 kHz) and magnetic field (0 $\leq H \leq$ 5 kOe). The dynamic scaling analysis of the relaxation time $\tau(T,H)$ defined as $\tau = 1/\omega$ at $T = T_{f}(H,\omega)$ suggests the absence of SG phase in the presence of $H$ (at least above 100 Oe). Dynamic scaling analysis of $\chi^{\prime \prime}(T, \omega)$ and $\tau(T,H)$ near $T_{g}$ leads to the critical exponents ($\beta$ = 0.36 $\pm$ 0.03, $\gamma$ = 3.5 $\pm$ 0.4, $\nu$ = 1.4 $\pm$ 0.2, $z$ = 6.6 $\pm$ 1.2, $\psi$ = 0.24 $\pm$ 0.02, and $\theta$ = 0.13 $\pm$ 0.02). The aging phenomenon is studied through the absorption $\chi^{\prime \prime}(\omega, t)$ below $T_{g}$. It obeys a $(\omega t)^{-b^{\prime \prime}}$ power-law decay with an exponent $b^{\prime \prime}\approx 0.15 - 0.2$. The rejuvenation effect is also observed under sufficiently large (temperature and magnetic-field) perturbations.Comment: 14 pages, 19 figures; to be published in Phys. Rev. B (September 1, 2003

No spin-glass transition in the "mobile-bond" model

The recently introduced ``mobile-bond'' model for two-dimensional spin glasses is studied. The model is characterized by an annealing temperature T_q. On the basis of Monte Carlo simulations of small systems it has been claimed that this model exhibits a non-trivial spin-glass transition at finite temperature for small values of T_q. Here the model is studied by means of exact ground-state calculations of large systems up to N=256^2. The scaling of domain-wall energies is investigated as a function of the system size. For small values T_q<0.95 the system behaves like a (gauge-transformed) ferromagnet having a small fraction of frustrated plaquettes. For T_q>=0.95 the system behaves like the standard two-dimensional +-J spin-glass, i.e. it does NOT exhibit a phase transition at T>0.Comment: 4 pages, 5 figures, RevTe

Aging and memory effects in beta-hydrochinone-clathrate

The out-of-equilibrium low-frequency complex susceptibility of the orientational glass methanol(73%)-beta-hydrochinone-clathrate is studied using temperature-stop protocols in aging experiments . Although the material does not have a sharp glass transition aging effects including rejuvenation and memory are found at low temperatures. However, they turn out to be much weaker, however, than in conventional magnetic spin glasses.Comment: 5 pages RevTeX, 6 eps-figures include

Extended droplet theory for aging in short-ranged spin glasses and a numerical examination

We analyze isothermal aging of a four dimensional Edwards-Anderson model in detail by Monte Carlo simulations. We analyze the data in the view of an extended version of the droplet theory proposed recently (cond-mat/0202110) which is based on the original droplet theory plus conjectures on the anomalously soft droplets in the presence of domain walls. We found that the scaling laws including some fundamental predictions of the original droplet theory explain well our results. The results of our simulation strongly suggest the separation of the breaking of the time translational invariance and the fluctuation dissipation theorem in agreement with our scenario.Comment: 27 pages, 39 epsfiles, revised versio

Generating droplets in two-dimensional Ising spin glasses by using matching algorithms

We study the behavior of droplets for two dimensional Ising spin glasses with Gaussian interactions. We use an exact matching algorithm which enables study of systems with linear dimension L up to 240, which is larger than is possible with other approaches. But the method only allows certain classes of droplets to be generated. We study single-bond, cross and a category of fixed volume droplets as well as first excitations. By comparison with similar or equivalent droplets generated in previous works, the advantages but also the limitations of this approach are revealed. In particular we have studied the scaling behavior of the droplet energies and droplet sizes. In most cases, a crossover of the data can be observed such that for large sizes the behavior is compatible with the one-exponent scenario of the droplet theory. Only for the case of first excitations, no clear conclusion can be reached, probably because even with the matching approach the accessible system sizes are still too small.Comment: 11 pages, 16 figures, revte

The two-dimensional random-bond Ising model, free fermions and the network model

We develop a recently-proposed mapping of the two-dimensional Ising model with random exchange (RBIM), via the transfer matrix, to a network model for a disordered system of non-interacting fermions. The RBIM transforms in this way to a localisation problem belonging to one of a set of non-standard symmetry classes, known as class D; the transition between paramagnet and ferromagnet is equivalent to a delocalisation transition between an insulator and a quantum Hall conductor. We establish the mapping as an exact and efficient tool for numerical analysis: using it, the computational effort required to study a system of width $M$ is proportional to $M^{3}$, and not exponential in $M$ as with conventional algorithms. We show how the approach may be used to calculate for the RBIM: the free energy; typical correlation lengths in quasi-one dimension for both the spin and the disorder operators; even powers of spin-spin correlation functions and their disorder-averages. We examine in detail the square-lattice, nearest-neighbour $\pm J$ RBIM, in which bonds are independently antiferromagnetic with probability $p$, and ferromagnetic with probability $1-p$. Studying temperatures $T\geq 0.4J$, we obtain precise coordinates in the $p-T$ plane for points on the phase boundary between ferromagnet and paramagnet, and for the multicritical (Nishimori) point. We demonstrate scaling flow towards the pure Ising fixed point at small $p$, and determine critical exponents at the multicritical point.Comment: 20 pages, 25 figures, figures correcte