Physical review. E最新文献

We study canonical-equilibrium properties of random field O(n) models involving classical continuous vector spins of n components with mean-field interactions and subject to disordered fields acting on individual spins. To this end, we employ two complementary approaches: the mean-field approximation, valid for any disorder distribution, and the replica trick, applicable when the disordered fields are sampled from a Gaussian distribution. On the basis of an exact analysis, we demonstrate that when replica symmetry holds, both the approaches yield identical expression for the free energy per spin of the system. As consequences, we study the case of n=2 (XY spins) and that of n=3 (Heisenberg spins) for two representative choices of the disorder distribution, namely, a Gaussian and a symmetric bimodal distribution. For both n=2 and n=3, we demonstrate that while the magnetization exhibits a continuous phase transition as a function of temperature for the Gaussian case, the transition could be either continuous or first order with an emergent tricriticality when the disorder distribution is bimodal. We also discuss in the context of our models the issue of self-averaging of extensive variables near the critical point of a continuous phase transition.

We numerically investigate the multicritical behavior of the three-dimensional lattice system in which a SU(2) gauge field is coupled to two flavors of scalar fields transforming in the fundamental representation of the gauge group. In this system, a multicritical point is present, where the global symmetry O(2)⊕O(3) gets enlarged to O(5). Such a symmetry enlargement is hindered for generic systems by the instability of the O(5) multicritical point, but the SU(2) gauge symmetry prevents the appearance of the term triggering the instability. All the numerical results obtained in this lattice gauge model fully support the expectations coming from the O(2)⊕O(3) multicritical Landau-Ginzburg-Wilson ϕ^{4} theory, and we discuss possible implications of these results for some models of deconfined quantum criticality.

We study an open quantum system of two qubits that are coupled by swapping interaction. Using the coupling strength between the qubits as a timescale, the Liouvillian of the system has exceptional points that depend on the disparity between the decay rates of the qubits. We find that the configuration of the initial states plays an important role in deciding the character of the entanglement dynamics at the initial stage of evolution. Depending on whether or not the initial excitations of the qubits can be swapped by the interaction that couples them, a change in the total decay rate can be either consistently unfavorable to entanglement generation, or shift the dynamics from hindering to enhancing entanglement generation, or vice versa, as the system traverses the exceptional points. The shift could also occur in a wide range of mixed states. We clarify the origin of the behavior in this work.

We propose a generative, mechanistic model of temporally evolving hypergraphs in which hyperedges form via noisy copying of previous hyperedges. Our proposed model reproduces several stylized facts from many empirical hypergraphs, is learnable from data, and defines a likelihood over a complete hypergraph rather than ego-based or other subhypergraphs. Analyzing our model, we derive asymptotic descriptions of the node degree, edge size, and edge intersection size distributions in terms of the model parameters. We also show several features of empirical hypergraphs which are and are not successfully captured by our model. We provide a scalable stochastic expectation maximization algorithm with which we can fit our model to hypergraph data sets with millions of nodes and edges. Finally, we assess our model on a hypergraph link prediction task, finding that an instantiation of our model with just 11 parameters can achieve competitive predictive performance with large neural networks.

Many physical systems, including some examples of active matter, granular assemblies, and biological systems, show fluctuation-dominated phase ordering (FDPO), where macroscopic fluctuations coexist with long-range order. Most of these systems are out of equilibrium. By contrast, a recent work has analytically demonstrated that an equilibrium one-dimensional truncated inverse distance square Ising (TIDSI) model shows FDPO. The analytical results rely on a cluster representation of the model that we term TIDSI-CL and are governed by the ratio, c, of the long-range interaction strength to the critical temperature. We show that the allowed range of c is very narrow in the original TIDSI model while it is unbounded in TIDSI-CL. We perform Monte Carlo simulations for the TIDSI model and show consistency with the analytical results in the allowed range of c. The correlation length grows strongly on approaching the critical point, leading to a broad near-critical region. Within this region, α, which is the cusp exponent of the power-law decay of the scaled correlation function at criticality, changes to α^{eff}. We also investigate the coarsening dynamics of the model: The correlation function, domain size distribution, and aging behavior are consistent with the equilibrium properties upon replacing the system size, L, by the coarsening length, L(t). The mean largest cluster size shows logarithmic corrections due to finite L and waiting time, t_{w}. The aging autocorrelation function exhibits two different scaling forms, characterized by exponents β and γ, at short and long times compared to t_{w}, where β=α/2.

We introduce a minimum Ising model with two different types of ferromagnetically interacting spin variables and the addition of chiral interactions according to the suggestions of the Dzyaloshinskii-Moryia mechanism to account for the onset of helical structures in magnetic systems. The investigation of the phase diagram on a Cayley tree is reduced to the analysis of the attractors of a discrete nonlinear map. This elementary system presents a complex phase behavior, which is reminiscent of the spatially modulated structures in the well-known axial next-nearest-neighbor Ising model of magnetism. We characterize the presence of some ordered as well as a certain number of modulated structures. Also, we sketch a layer-by-layer mean-field calculation for the phase diagram of a similar monoaxial Ising system on a cubic lattice.

To accurately represent disease spread, epidemiological models must account for the complex network topology and contact heterogeneity. Traditionally, most studies have used random heterogeneous networks, which ignore correlations between the nodes' degrees. Yet, many real-world networks exhibit degree assortativity-the tendency for nodes with similar degrees to connect. Here we explore the effect degree assortativity (or disassortativity) has on long-term dynamics and disease extinction in the realm of the susceptible-infected-susceptible model on heterogeneous networks. We derive analytical results for the mean time to extinction (MTE) in assortative networks with weak heterogeneity, and show that increased assortativity reduces the MTE and that assortativity and degree heterogeneity are interchangeable with regard to their impact on the MTE. Our analytical results are verified using the weighted ensemble numerical method, on both synthetic and real-world networks. Notably, this method allows us to go beyond the capabilities of traditional numerical tools, enabling us to study rare events in large assortative networks, which were previously inaccessible.

We investigate the effects of microalloying via random pinning on the yielding transition under oscillatory shear through extensive computer simulations. Random pinning refers to freezing the relaxation degrees of freedom for a fraction of randomly selected particles, which is often termed as hard pinning. Experimentally, pinning effects can be realized by introducing particles with much larger masses and diameters than the particles in the host medium, which is termed soft pinning. Many multicomponent glasses, especially metallic glasses, are good examples of such systems in which the mass and sizes of constituent molecules can vary considerably. Large molecules in these systems can act like soft pinning particles with respect to other particles due to a large timescale separation in their relaxation process. Using the Kob-Andersen model as our glass former, we create a randomly pinned system by pinning a fraction of the particles permanently, as well as by increasing their masses, thereby creating soft pinning sites. Increasing the fraction of hard or soft pinned particles transforms the system from a fragile to a strong glass former, enabling a systematic investigation of how fragility influences the yielding transition. Our findings reveal significant differences in the yielding behavior between strong and fragile glasses. These findings, along with earlier studies where fragility was tuned by varying the packing fraction in soft-sphere systems, demonstrate a universal relationship between fragility and yielding. Moreover, by varying the spatial dimensions, we demonstrate that the relationship is independent of both the dimensionality and the underlying origin of fragility in these model systems.

The spring network model constitutes the backbone in the representations of a host of physical systems. In this work, we report the disturbance-driven microscopic dynamics of an isolated, closed spring network of spherical topology in mechanical equilibrium. The system permits self-intersection. We first show the lowest-energy configurations of the closed spring networks as packings of regular triangles. The dynamics of the disturbed spring network is analyzed from the multiple perspectives of energetics, structural instability, and speed distribution. We reveal the crumpling transition of strongly disturbed spring networks and the rapid convergence of the speed distribution toward the Maxwell-Boltzmann distribution. This work demonstrates the rich physics arising from the interplay of flexibility and dynamics. The results may yield insights into the shape fluctuation and structural instability of deformable membranes from the dynamical perspective.

We derive an analytical expression for the propagator and the transition path time distribution of a two-dimensional active Brownian particle crossing a parabolic barrier with absorbing boundary conditions at both sides. By taking those of a passive Brownian particle as basis states and dealing with the activity as a perturbation, our solution is expressed in terms of the perturbed eigenfunctions and eigenvalues of the associated Fokker-Planck equation once the latter is reduced by taking into account only the coordinate along the direction of the barrier and the self-propulsion angle. We show that transition path times are typically shortened by the self-propulsion of the particle. Our solution also allows us to obtain the survival probability and the first-passage times distribution, which display a strong dependence on the particle's activity, while the rotational diffusivity influences them to a minor extent.