Numerical Study of Competing Spin-Glass and Ferromagnetic Order

Two and three dimensional random Ising models with a Gaussian distribution of couplings with variance $J$ and non-vanishing mean value $J_0$ are studied using the zero-temperature domain-wall renormalization group (DWRG). The DWRG trajectories in the ($J_0,J$) plane after rescaling can be collapsed on two curves: one for $J_0/J > r_c$ and other for $J_0/J < r_c$. In the first case the DWRG flows are toward the ferromagnetic fixed point both in two and three dimensions while in the second case flows are towards a paramagnetic fixed point and spin-glass fixed point in two and three dimensions respectively. No evidence for an extra phase is found.Comment: a bit more data is taken, 5 pages, 4 eps figures included, to appear in PR

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.

Calculation of ground states of four-dimensional +or- J Ising spin glasses

Ground states of four-dimensional (d=4) EA Ising spin glasses are calculated for sizes up to 7x7x7x7 using a combination of a genetic algorithm and cluster-exact approximation. The ground-state energy of the infinite system is extrapolated as e_0=-2.095(1). The ground-state stiffness (or domain wall) energy D is calculated. A D~L^{\Theta} behavior with \Theta=0.65(4) is found which confirms that the d=4 model has an equilibrium spin-glass-paramagnet transition for non-zero T_c.Comment: 5 pages, 3 figures, 31 references, revtex; update of reference

Lower Critical Dimension of Ising Spin Glasses

Exact ground states of two-dimensional Ising spin glasses with Gaussian and bimodal (+- J) distributions of the disorder are calculated using a ``matching'' algorithm, which allows large system sizes of up to N=480^2 spins to be investigated. We study domain walls induced by two rather different types of boundary-condition changes, and, in each case, analyze the system-size dependence of an appropriately defined ``defect energy'', which we denote by DE. For Gaussian disorder, we find a power-law behavior DE ~ L^\theta, with \theta=-0.266(2) and \theta=-0.282(2) for the two types of boundary condition changes. These results are in reasonable agreement with each other, allowing for small systematic effects. They also agree well with earlier work on smaller sizes. The negative value indicates that two dimensions is below the lower critical dimension d_c. For the +-J model, we obtain a different result, namely the domain-wall energy saturates at a nonzero value for L\to \infty, so \theta = 0, indicating that the lower critical dimension for the +-J model exactly d_c=2.Comment: 4 pages, 4 figures, 1 table, revte

Growth Kinetics in a Phase Field Model with Continuous Symmetry

We discuss the static and kinetic properties of a Ginzburg-Landau spherically symmetric $O(N)$ model recently introduced (Phys. Rev. Lett. {\bf 75}, 2176, (1995)) in order to generalize the so called Phase field model of Langer. The Hamiltonian contains two $O(N)$ invariant fields $\phi$ and $U$ bilinearly coupled. The order parameter field $\phi$ evolves according to a non conserved dynamics, whereas the diffusive field $U$ follows a conserved dynamics. In the limit $N \to \infty$ we obtain an exact solution, which displays an interesting kinetic behavior characterized by three different growth regimes. In the early regime the system displays normal scaling and the average domain size grows as $t^{1/2}$, in the intermediate regime one observes a finite wavevector instability, which is related to the Mullins-Sekerka instability; finally, in the late stage the structure function has a multiscaling behavior, while the domain size grows as $t^{1/4}$.Comment: 9 pages RevTeX, 9 figures included, files packed with uufiles to appear on Phy. Rev.

Low Energy Excitations in Spin Glasses from Exact Ground States

We investigate the nature of the low-energy, large-scale excitations in the three-dimensional Edwards-Anderson Ising spin glass with Gaussian couplings and free boundary conditions, by studying the response of the ground state to a coupling-dependent perturbation introduced previously. The ground states are determined exactly for system sizes up to 12^3 spins using a branch and cut algorithm. The data are consistent with a picture where the surface of the excitations is not space-filling, such as the droplet or the ``TNT'' picture, with only minimal corrections to scaling. When allowing for very large corrections to scaling, the data are also consistent with a picture with space-filling surfaces, such as replica symmetry breaking. The energy of the excitations scales with their size with a small exponent \theta', which is compatible with zero if we allow moderate corrections to scaling. We compare the results with data for periodic boundary conditions obtained with a genetic algorithm, and discuss the effects of different boundary conditions on corrections to scaling. Finally, we analyze the performance of our branch and cut algorithm, finding that it is correlated with the existence of large-scale,low-energy excitations.Comment: 18 Revtex pages, 16 eps figures. Text significantly expanded with more discussion of the numerical data. Fig.11 adde

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

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

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

A Soluble Phase Field Model

The kinetics of an initially undercooled solid-liquid melt is studied by means of a generalized Phase Field model, which describes the dynamics of an ordering non-conserved field phi (e.g. solid-liquid order parameter) coupled to a conserved field (e.g. thermal field). After obtaining the rules governing the evolution process, by means of analytical arguments, we present a discussion of the asymptotic time-dependent solutions. The full solutions of the exact self-consistent equations for the model are also obtained and compared with computer simulation results. In addition, in order to check the validity of the present model we confronted its predictions against those of the standard Phase field model and found reasonable agreement. Interestingly, we find that the system relaxes towards a mixed phase, depending on the average value of the conserved field, i.e. on the initial condition. Such a phase is characterized by large fluctuations of the phi field.Comment: 13 pages, 8 figures, RevTeX 3.1, submitted to Physical Review