Closure of the Monte Carlo dynamical equation in the spherical Sherrington-Kirkpatrick model

We study the analytical solution of the Monte Carlo dynamics in the spherical Sherrington-Kirkpatrick model using the technique of the generating function. Explicit solutions for one-time observables (like the energy) and two-time observables (like the correlation and response function) are obtained. We show that the crucial quantity which governs the dynamics is the acceptance rate. At zero temperature, an adiabatic approximation reveals that the relaxational behavior of the model corresponds to that of a single harmonic oscillator with an effective renormalized mass.

Fragile-glass behavior of a short-range p-spin model

We propose a short-range generalization of the p-spin interaction spin-glass model. The model is well suited to test the idea that an entropy collapse is at the bottom line of the dynamical singularity encountered in structural glasses. The model is studied in three dimensions through Monte Carlo simulations, which put in evidence fragile glass behavior with stretched exponential relaxation and super-Arrhenius behavior of the relaxation time. Our data are in favor of a Vogel-Fulcher behavior of the relaxation time, related to an entropy collapse at the Kauzmann temperature. We, however, encounter difficulties analogous to those found in experimental systems when extrapolating thermodynamical data at low temperatures. We study the spin-glass susceptibility, investigating the behavior of the correlation length in the system. We find that the increase of the relaxation time is accompanied by a very slow growth of the correlation length. We discuss the scaling properties of off-equilibrium dynamics in the glassy regime, finding qualitative agreement with the mean-field theory.

Chaotic, memory, and cooling rate effects in spin glasses: Evaluation of the Edwards-Anderson model

We investigate chaotic, memory, and cooling rate effects in the three-dimensional Edwards-Anderson model by doing thermoremanent (TRM) and ac susceptibility numerical experiments and making a detailed comparison with laboratory experiments on spin glasses. In contrast to the experiments, the Edwards-Anderson model does not show any trace of reinitialization processes in temperature change experiments (TRM or ac). A detailed comparison with ac relaxation experiments in the presence of dc magnetic field or coupling distribution perturbations reveals that the absence of chaotic effects in the Edwards-Anderson model is a consequence of the presence of strong cooling rate effects. We discuss possible solutions to this discrepancy, in particular the smallness of the time scales reached in numerical experiments, but we also question the validity of the Edwards-Anderson model to reproduce the experimental results.

Squared interaction matrix Sherrington-Kirkpatrick model for a spin glass

The mean-field theory of a spin glass with a specific form of nearest- and next-nearest-neighbor interactions is investigated. Depending on the sign of the interaction matrix chosen we find either the continuous replica symmetry breaking seen in the Sherrington-Kirkpartick model or a one-step solution similar to that found in structural glasses. Our results are confirmed by numerical simulations and the link between the type of spin-glass behavior and the density of eigenvalues of the interaction matrix is discussed.

Giant heat dissipation at the low temperature reversible-irreversible transition in Gd5Ge4

The heat exchanged at the low-temperature first-order magnetostructural transition is directly measured in Gd5Ge4 . Results show that the origin and the temperature dependence of the heat exchanged varies with the reversible/irreversible character of the first-order transition. In the reversible regime, the heat exchanged by the sample is mostly due to the latent heat at the transition and decreases with decreasing temperature, while in the irreversible regime, the heat is irreversibly dissipated and increases strongly with decreasing temperature, reaching a value of 237 J/kg at 4 K.

Reply to "Comment on 'Nature and entropy content of the ordering transitions in RCo2'"

In the previous Comment, Forker and co-workers claim that perturbed angular correlation (PAC) data leave no alternative to the conclusion that the spontaneous magnetization of PrCo2 and NdCo2 undergoes a discontinuous, first-order phase transition at TC. We show here that their claim is in clear contradiction with a wealth of experimental evidence, including our own. Finally, we propose a possible origin for the disagreement between their interpretation of the PAC results and the literature on this subject.

Competitive sorption and desorption of phosphate and citrate in clayey and sandy loam soils

The increase of organic acids in soils can reduce phosphorus sorption. The objective of the study was to evaluate the competitive sorption of P and citrate in clayey and sandy loam soils, using a stirred-flow system. Three experiments were performed with soil samples (0-20 cm layer) of clayey (RYL-cl) and sandy loam (RYL-sl) Red Yellow Latosols (Oxisols). In the first study, the treatments were arranged in a 2 × 5 factorial design, with two soil types and five combinations of phosphorus and citrate application (only P; P + citrate; and citrate applied 7, 22, 52 min before P); in the second, the treatments were arranged in a 2 × 2 factorial design, corresponding to two soils and two forms of P and citrate application (only citrate and citrate + P); and in the third study, the treatments in a 2 × 2 × 6 factorial design consisted of two soils, two extractors (citrate and water) and six incubation times. In the RYL-cl and RYL-sl, P sorption was highest (44 and 25 % of P application, respectively), in the absence of citrate application. Under citrate application, P sorption was reduced in all treatments. The combined application of citrate and P reduced P sorption to 25.8 % of the initially applied P in RYL-cl and to 16.7 % in RYL-sl, in comparison to P without citrate. Citrate sorption in RYL-cl and RYL-sl was highest in the absence of P application, corresponding to 32.0 and 30.2 % of the citrate applied, respectively. With P application, citrate sorption was reduced to 26.4 and 19.7 % of the initially applied citrate in RYL-cl and RYL-sl, respectively. Phosphorus desorption was greater when citrate was used. Phosphorus desorption with citrate and water was higher in the beginning (until 24 h of incubation of P) in RYL-cl and RYL-sl, indicating a rapid initial phase, followed by a slow release phase. This suggests that according to the contact time of P with the soil colloids, the previously adsorbed P can be released to the soil solution in the presence of competing ligands such as citrate. In conclusion, a soil management with continuous input of organic acids is desirable, in view of their potential to compete for P sorption sites, especially in rather weathered soils.

Effect of potassium fertilization on yield and nutrition of yerba mate (Ilex paraguariensis)

Yerba mate (Ilex paraguariensis) is a tree species native to the subtropical regions of South America, and is found in Brazil predominantly in the southern region. Despite the historical importance in this region, so far, studies on crop nutrition to improve yields are scarce. Thus, this study evaluated the effect of potassium rates on K soil availability, and the yield and nutritional status of yerba mate. The experiment was conducted in São Mateus do Sul, State of Paraná, on a Humox soil, where K2O rates of 0, 20, 40, 80, 160, and 320 kg ha-1 were tested on 7-year-old plantations. The experiment was harvested 24 months after installation by removing approximately 95 % of the canopy that had sprouted from the previous harvest. The soil was evaluated for K availability in the layers 0-10, 0-20, 10-20, and 20-40 cm. The plant parts leaf fresh matter (LM), twigs (TW), thick branches (BR) and commercial yerba mate (COYM), i.e., LM+TW, were analyzed. In addition, the relationship between fresh matter/dry matter (FM/DM) and K concentration in LM, AG and BR were evaluated. The fertilization increased K availability in all evaluated soil layers, indicating good mobility of the nutrient even at low rates. Yerba mate responded positively to increasing K2O rates with higher yields of all harvested components. The crop proved K-demanding, with a maximum COYM yield of 28.5 t ha-1, when 72 mg dm-3 K was available in the 0-20 cm layer. Yerba mate in the plant production stage requires soil K availability at medium to high level; in clayey soil with low K availability, a rate of 300 kg ha-1 K2O should be applied at 24 month intervals to obtain high yields. A leaf K concentration of 16.0 g ha-1 is suitable for yerba mate in the growth stage.

Solvable dynamics in a system of interacting random tops

A new solvable model of synchronization dynamics is introduced. It consists of a system of long range interacting tops or magnetic moments with random precession frequencies. The model allows for an explicit study of orientational effects in synchronization phenomena as well as nonlinear processes in resonance phenomena in strongly coupled magnetic systems. A stability analysis of the incoherent solution is performed for different types of orientational disorder. A system with orientational disorder always synchronizes in the absence of noise.

Exactly solvable phase oscillator models with syncrhonization dynamics

Populations of phase oscillators interacting globally through a general coupling function f(x) have been considered. We analyze the conditions required to ensure the existence of a Lyapunov functional giving close expressions for it in terms of a generating function. We have also proposed a family of exactly solvable models with singular couplings showing that it is possible to map the synchronization phenomenon into other physical problems. In particular, the stationary solutions of the least singular coupling considered, f(x) = sgn(x), have been found analytically in terms of elliptic functions. This last case is one of the few nontrivial models for synchronization dynamics which can be analytically solved.

General method to determine replica symmetry breaking transitions

We introduce a new parameter to investigate replica symmetry breaking transitions using finite-size scaling methods. Based on exact equalities initially derived by F. Guerra this parameter is a direct check of the self-averaging character of the spin-glass order parameter. This new parameter can be used to study models with time reversal symmetry but its greatest interest lies in models where this symmetry is absent. We apply the method to long-range and short-range Ising spin-glasses with and without a magnetic field as well as short-range multispin interaction spin-glasses.

Glassiness in a model without energy barriers

We propose a microscopic model without energy barriers in order to explain some generic features observed in structural glasses. The statics can be exactly solved while the dynamics has been clarified using Monte Carlo calculations. Although the model has no thermodynamic transition, it captures some of the essential features of real glasses, i.e., extremely slow relaxation, time dependent hysteresis effects, anomalous increase of the relaxation time, and aging. This suggests that the effect of entropy barriers can be an important ingredient to account for the behavior observed in real glasses.