Phase separation kinetics and cluster dynamics in two-dimensional active dumbbell systems

Molecular dynamics simulations were employed to investigate the phase separation process of a two-dimensional active Brownian dumbbell model. We evaluated the time dependence of the typical size of the dense component using the scaling properties of the structure factor, along with the averaged number of clusters and their radii of gyration. The growth observed is faster than in active disk models, and this effect is further enhanced under stronger activity. Next, we focused on studying the hexatic order of the clusters. The length associated with the orientational order increases algebraically with time and faster than for spherical active Brownian particles. Under weak active forces, most clusters exhibit a uniform internal orientational order. However, under strong forces, large clusters consist of domains with different orientational orders. We demonstrated that the latter configurations are not stable, and given sufficient time to evolve, they eventually achieve homogeneous configurations as well. No gas bubbles are formed within the clusters, even when there are patches of different hexatic order. Finally, attention was directed towards the geometry and motion of the clusters themselves. By employing a tracking algorithm, we showed that clusters smaller than the typical size at the observation time exhibit regular shapes, while larger ones display fractal characteristics. In between collisions or break-ups, the clusters behave as solid bodies. Their centers of mass undergo circular motion, with radii increasing with the cluster size. The angular velocity of the center of mass equals that of the constituents with respect to their center of mass. These observations were rationalised with a simple mechanical model.

Phase behaviour and dynamics of three-dimensional active dumbbell systems

We present a comprehensive numerical study of the phase behavior and dynamics of a three-dimensional active dumbbell system with attractive interactions. We demonstrate that attraction is essential for the system to exhibit nontrivial phases. We construct a detailed phase diagram by exploring the effects of the system's activity, density, and attraction strength. We identify several distinct phases, including a disordered, a gel, and a completely phase-separated phase. Additionally, we discover a novel dynamical phase, that we name percolating network, which is characterized by the presence of a spanning network of connected dumbbells. In the phase-separated phase we characterize numerically and describe analytically the helical motion of the dense cluster.

Field-Tuned Order by Disorder in Frustrated Ising Magnets with Antiferromagnetic Interactions

We demonstrate the appearance of thermal order by disorder in Ising pyrochlores with staggered antiferromagnetic order frustrated by an applied magnetic field. We use a mean-field cluster variational method, a low-temperature expansion, and Monte Carlo simulations to characterize the order-by-disorder transition. By direct evaluation of the density of states, we quantitatively show how a symmetry-broken state is selected by thermal excitations. We discuss the relevance of our results to experiments in 2D and 3D samples and evaluate how anomalous finite-size effects could be exploited to detect this phenomenon experimentally in two-dimensional artificial systems, or in antiferromagnetic all-in-all-out pyrochlores like Nd_{2}Hf_{2}O_{7} or Nd_{2}Zr_{2}O_{7}, for the first time.

Out-of-equilibrium dynamical fluctuations in glassy systems

In this paper we extend the earlier treatment of out-of-equilibrium mesoscopic fluctuations in glassy systems in several significant ways. First, via extensive simulations, we demonstrate that models of glassy behavior without quenched disorder display scalings of the probability of local two-time correlators that are qualitatively similar to that of models with short-ranged quenched interactions. The key ingredient for such scaling properties is shown to be the development of a criticallike dynamical correlation length, and not other microscopic details. This robust data collapse may be described in terms of a time-evolving "extreme value" distribution. We develop a theory to describe both the form and evolution of these distributions based on a effective sigma model approach.

Cluster expansions in dilute systems: applications to satisfiability problems and spin glasses

We develop a systematic cluster expansion for dilute systems in the highly dilute phase. We first apply it to the calculation of the entropy of the K-satisfiability problem in the satisfiable phase. We derive a series expansion in the control parameter, the average connectivity, that is identical to the one obtained by using the replica approach with a replica symmetric (RS) ansatz, when the order parameter is calculated via a perturbative expansion in the control parameter. As a second application we compute the free energy of the Viana-Bray model in the paramagnetic phase. The cluster expansion allows one to compute finite-size corrections in a simple manner, and these are particularly important in optimization problems. Importantly enough, these calculations prove the exactness of the RS ansatz below the percolation threshold, and might require its revision between this and the easy-to-hard transition.

Glassy systems under time-dependent driving forces: application to slow granular rheology

We study the dynamics of a glassy model with infinite range interactions externally driven by an oscillatory force. We find a well-defined transition in the (temperature-amplitude-frequency) phase diagram between (i) a "glassy" state characterized by the slow relaxation of one-time quantities, aging in two-time quantities and a modification of the equilibrium fluctuation-dissipation relation; and (ii) a "liquid" state with a finite relaxation time. In the glassy phase, the degrees of freedom governing the slow relaxation are thermalized to an effective temperature. Using Monte Carlo simulations, we investigate the effect of trapping regions in phase space on the driven dynamics. We find that it alternates between periods of rapid motion and periods of trapping. These results confirm the strong analogies between the slow granular rheology and the dynamics of glasses. They also provide a theoretical underpinning to earlier attempts to present a thermodynamic description of moderately driven granular materials.

Hole-burning experiments within glassy models with infinite range interactions

We reproduce the results of nonresonant spectral hole-burning experiments with glassy models with infinite-range interactions that generalize the mode-coupling approach to nonequilibrium situations. We show that an ac field modifies the integrated linear response and the correlation in a way that depends on the amplitude and frequency of the pumping field. We study the effect of the waiting and recovery times and the number of oscillations applied. This calculation will help discriminate which results can and which cannot be attributed to spatial heterogeneities in real systems.

From second to first order transitions in a disordered quantum magnet

We study the spin-glass transition in a disordered quantum model. In a region of the phase diagram quantum effects are small and the phase transition is second order, as in the classical case. In another region, quantum fluctuations drive the transition to first order. Across the first order line the susceptibility is discontinuous and shows hysteresis. Our findings qualitatively reproduce observations on LiHoxY1-xF4. We also discuss a marginally stable spin-glass state and derive some results previously obtained from the real-time dynamics of the model coupled to a bath.

Correlated Attractors from Uncorrelated Stimuli

Analytic results for a neural network model proposed to account for neurophysiological experiments in which attractors for uncorrelated patterns are found to be correlated are presented. Exact expressions for the associative attractors and their correlations are described.