Magnetoelectric properties of a coupled spin-electron model on a doubly decorated square lattice in an external electric field applied along the crystallographic axis [11] are rigorously examined with the help of generalized decoration-iteration transformation. The phase diagram, spontaneous magnetization and electric polarization are exactly calculated and their dependencies are comprehensively investigated under a concurrent influence of temperature and electric field. It is found that the electric field mostly stabilizes at zero temperature the spontaneous antiferromagnetic order with respect to the ferromagnetic one. At finite temperatures the external electric field gradually suppresses a spontaneous ferromagnetic (antiferromagnetic) order emergent close to a quarter (half) filling. An enhanced magnetoelectric response is detectable in the vicinity of a continuous phase transition at which the spontaneous magnetization vanishes and the electric polarization displays a weak-type singularity. It is demonstrated that reentrant phase transitions of the ferromagnetic or antiferromagnetic phase may be induced at moderate values of the electric field, which simultaneously produces a sharp kink in a critical line of the ferromagnetic phase nearby a quarter filling.

To explore how the topology of interaction networks determines the robustness of dynamical systems, we study the antisymmetric Lotka-Volterra equation (ALVE). The ALVE is the replicator equation of zero-sum games in evolutionary game theory, in which the strengths of pairwise interactions between strategies are defined by an antisymmetric matrix such that typically some strategies go extinct over time. Here we show that there also exist topologically robust zero-sum games, such as the rock-paper-scissors game, for which all strategies coexist for all choices of interaction strengths. We refer to such zero-sum games as coexistence networks and construct coexistence networks with an arbitrary number of strategies. By mapping the long-time dynamics of the ALVE to the algebra of antisymmetric matrices, we identify simple graph-theoretical rules by which coexistence networks are constructed. Examples are triangulations of cycles characterized by the golden ratio $\phi =1.6180...$, cycles with complete subnetworks, and non-Hamiltonian networks. In graph-theoretical terms, we extend the concept of a Pfaffian orientation from even-sized to odd-sized networks. Our results show that the topology of interaction networks alone can determine the long-time behavior of nonlinear dynamical systems, and may help to identify robust network motifs arising, for example, in ecology.

We reveal large fluctuations in the response of real multiplex networks to random damage of nodes. These results indicate that the average response to random damage, traditionally considered in mean-field approaches to percolation, is a poor metric of system robustness. We show instead that a large-deviation approach to percolation provides a more accurate characterization of system robustness. We identify an effective percolation threshold at which we observe a clear abrupt transition separating two distinct regimes in which the most likely response to damage is either a functional or a dismantled multiplex network. We leverage our findings to propose a metric, named safeguard centrality, able to single out the nodes that control the response of the entire multiplex network to random damage. We show that safeguarding the function of top-scoring nodes is sufficient to prevent system collapse.

We report experimental studies on the temperature-dependent translational and rotational viscosities of a few nematic liquid crystals made of highly polar molecules. Cyanobiphenyl (nCB) with longitudinal and cyanobicyclohexane molecules (CCN-mn) with transverse dipole moments were chosen and the measurements were made in the nematic phase. The translational viscosity (shear viscosity) is measured by using a rheometer and the rotational viscosity is measured from the dynamics of the Freedericksz transition by measuring the optical phase-retardation decay of the sample. The associated activation energies are obtained from the fitting of the appropriate equation in the nematic phase. Only 8CB and CCN-47 exhibits N to Sm-A phase transition and their activation energies of translational and rotational viscosities are larger compared to the shortest homologs in the respective series. Both activation energies of 8CB are significantly larger than that of CCN-47. The temperature-dependent steady states of the director distribution under shear are comprehensibly reflected in the rheodielectric measurements of 8CB than that of CCN-47. The results are explained based on the differences in the Sm-A short-range orders and the critical slowing down of the order parameter fluctuations. We present a simple physical model of molecular association that gives rise to different Sm-A short-range orders in both classes of compounds.

The emergence of quantum statistical mechanics from individual pure states of closed many-body systems is under intensive investigation. While most effort has been put on the impact of the direct interaction (i.e., the usual mutual interaction), here we study systematically and analytically the impact of the exchange interaction that arises from the particle indistinguishability. We show that this interaction leads an overwhelming number of Fock states to exhibit a structure that can be resolved only by observables adjusted according to the system's dynamical properties and from which thermal distributions emerge. This hidden thermal structure in Fock space is found to be related to the so-called limit shape of random geometric objects in mathematics. The structure enables us to uncover, for both ideal and nonideal Fermi gases, a striking mechanism for the emergence of quantum statistical mechanics from individual eigenstates.

A relationship based upon analogy is explored between (i) a lattice-based model for percolation by cylinders that employs distinct site types with unequal occupation probabilities in order to capture heterogeneities in the particle dispersion, and (ii) the well-studied mean-field lattice gas model. The strength of the correlation that sites in the percolation model that have distinct occupation probabilities are adjacent to each other maps into the coupling constant for the associated lattice fluid problem. Pursuing the analogy further, the vapor-liquid coexistence curve for the lattice gas translates into a phase boundary for the percolation problem, in terms of a locus of correlation strengths that demarcate a region of phase separation into sites with different occupation probabilities and distinct percolation thresholds. The dependence of the percolation thresholds in the one- and two-phase regions as delineated by this analogy are calculated as functions of the degree of disparity between site occupation probabilities and the strength of the correlation between adjacent site types.

We study field-induced phase transitions in the two-dimensional dipolar Ising ferromagnet with a specific ratio between the exchange and dipolar constants, $\delta =1$, which exhibits a stripe-ordered phase with the width of one lattice unit at low temperatures without magnetic field. By using a mean-field (MF) approximation and a Monte Carlo (MC) method with the stochastic-cutoff algorithm, which is an $O\left(N\right)$ simulation method, we show the temperature-field phase diagrams. In the MC study the orientational order and the structure factor are evaluated. Second-order transition points are determined by a finite-size-scaling analysis and first-order transition points are identified by the analysis of the energy histogram. Although both the MF and MC phase diagrams consist of wide regions of several stripe-ordered phases and narrow regions between them characterized by complicated stripe patterns, they show qualitative and quantitative differences in possible phases and phase boundaries. In the MF phase diagram, three main stripe-ordered phases exhibit a nesting structure, while in the MC phase diagram, two main stripe-ordered phases are located separately, which causes a characteristic field-induced reentrant transition of the orientational order. To our knowledge, this is the first observation of the reentrant phase transition in the dipolar Ising ferromagnet.

We consider the collective behavior of active particles that locally align with their neighbors. Agent-based simulation models have previously shown that in one dimension, these particles can form into a flock that maintains its stability by stochastically alternating its direction. Until now, this behavior has been seen in models based on continuum field equations only by appealing to long-range interactions that are not present in the simulation model. Here, we derive a set of stochastic field equations with local interactions that reproduces both qualitatively and quantitatively the behavior of the agent-based model, including the alternating flock phase. A crucial component is a multiplicative noise term of the voter model type in the dynamics of the local polarization whose magnitude is inversely proportional to the local density. We show that there is an important subtlety in determining the physically appropriate noise, in that it depends on a careful choice of the field variables used to characterize the system. We further use the resulting equations to show that a nonlinear alignment interaction of at least cubic order is needed for flocking to arise.

We provide arguments for the property of the degree-degree correlations of giant components formed by the percolation process on uncorrelated random networks. Using the generating functions, we derive a general expression for the assortativity of a giant component, $r$, which is defined as Pearson's correlation coefficient for degrees of directly connected nodes. For uncorrelated random networks in which the third moment for the degree distribution is finite, we prove the following two points: (1) Assortativity $r$ satisfies the relation $r\le 0$ for $p\ge p_{\mathrm{c}}$. (2) The average degree of nodes adjacent to degree $k$ nodes at the percolation threshold is proportional to $k^{-1}$ independently of the degree distribution function. These results claim that disassortativity emerges in giant components near the percolation threshold. The accuracy of the analytical treatment is confirmed by extensive Monte Carlo simulations.

Time-varying network topologies can deeply influence dynamical processes mediated by them. Memory effects in the pattern of interactions among individuals are also known to affect how diffusive and spreading phenomena take place. In this paper we analyze the combined effect of these two ingredients on epidemic dynamics on networks. We study the susceptible-infected-susceptible (SIS) and the susceptible-infected-recovered (SIR) models on the recently introduced activity-driven networks with memory. By means of an activity-based mean-field approach, we derive, in the long-time limit, analytical predictions for the epidemic threshold as a function of the parameters describing the distribution of activities and the strength of the memory effects. Our results show that memory reduces the threshold, which is the same for SIS and SIR dynamics, therefore favoring epidemic spreading. The theoretical approach perfectly agrees with numerical simulations in the long-time asymptotic regime. Strong aging effects are present in the preasymptotic regime and the epidemic threshold is deeply affected by the starting time of the epidemics. We discuss in detail the origin of the model-dependent preasymptotic corrections, whose understanding could potentially allow for epidemic control on correlated temporal networks.

It has been shown recently that changing the fluidic properties of a drug can improve its efficacy in ablating solid tumors. We develop a modeling framework for tumor ablation and present the simplest possible model for drug diffusion in a porous spherical tumor with leaky boundaries and assuming cell death eventually leads to ablation of that cell effectively making the two quantities numerically equivalent. The death of a cell after a given exposure time depends on both the concentration of the drug and the amount of oxygen available to the cell, which we assume is the same throughout the tumor for further simplicity. It can be assumed that a minimum concentration is required for a cell to die, effectively connecting diffusion with efficacy. The concentration threshold decreases as exposure time increases, which allows us to compute dose-response curves. Furthermore, these curves can be plotted at much finer time intervals compared to that of experiments, which may possibly be used to produce a dose-threshold-response surface giving an observer a complete picture of the drug's efficacy for an individual. In addition, since the diffusion, leak coefficients, and the availability of oxygen is different for different individuals and tumors, we produce artificial replication data through bootstrapping to simulate error. While the usual data-driven model with sigmoidal curves use 12 free parameters, our mechanistic model only has two free parameters, allowing it to be open to scrutiny rather than forcing agreement with data. Even so, the simplest model in our framework, derived here, shows close agreement with the bootstrapped curves and reproduces well-established relations, such as Haber's rule.

Using Monte Carlo simulations, we investigate the electrical conductivity of networks of hard rods with aspect ratios 10 and 20 as a function of the volume fraction for two tunneling conductance models. For a simple, orientationally independent tunneling model, we observe nonmonotonic behavior of the bulk conductivity as a function of volume fraction at the isotropic-nematic transition. However, this effect is lost if one allows for anisotropic tunneling. The relative conductivity enhancement increases exponentially with volume fraction in the nematic phase. Moreover, we observe that the orientational ordering of the rods in the nematic phase induces an anisotropy in the conductivity, i.e., enhanced values in the direction of the nematic director field. We also compute the mesh number of the Kirchhoff network, which turns out to be a simple alternative to the computationally expensive conductivity of large systems in order to get a qualitative estimate.

Spin glasses have competing interactions and complex energy landscapes that are highly susceptible to perturbations, such as the temperature or the bonds. The thermal boundary condition technique is an effective and visual approach for characterizing chaos and has been successfully applied to three dimensions. In this paper, we tailor the technique to partial thermal boundary conditions, where the thermal boundary condition is applied in a subset (three out of four in this work) of the dimensions for better flexibility and efficiency for a broad range of disordered systems. We use this method to study both temperature chaos and bond chaos of the four-dimensional Edwards-Anderson model with Gaussian disorder to low temperatures. We compare the two forms of chaos, with chaos of three dimensions, and also the four-dimensional $\pm J$ model. We observe that the two forms of chaos are characterized by the same set of scaling exponents, bond chaos is much stronger than temperature chaos, and the exponents are also compatible with the $\pm J$ model. Finally, we discuss the effects of chaos on the number of pure states in the thermal boundary condition ensemble.

The object of the present article is a one-dimensional lattice-gas model of soft particles, wherein particles interact only if they occupy the same or a neighboring site. The model is intended as a simple representation of penetrable particles of soft condensed matter. To represent different scenarios, two different realizations of the lattice model are considered: a one-component and a two-component system. For the two-component case particles of the same species repel and those of opposite species attract each other. The systems are analyzed entirely within the transfer matrix framework. Special attention is paid to the criterion devised in Ref. [Phys. Rev. E 63, 031206 (2001)], which serves to separate two types of behavior encountered in one-component penetrable particle systems. In addition to confirm the existence of a similar criterion in the one-component lattice-gas model, we find that the same criterion can be used in the two-component system for predicting the occurrence of thermodynamic catastrophe.

How individuals adapt their behavior in cultural evolution remains elusive. Theoretical studies have shown that the update rules chosen to model individual decision making can dramatically modify the evolutionary outcome of the population as a whole. This hints at the complexities of considering the personality of individuals in a population, where each one uses its own rule. Here, we investigate whether and how heterogeneity in the rules of behavior update alters the evolutionary outcome. We assume that individuals update behaviors by aspiration-based self-evaluation and they do so in their own ways. Under weak selection, we analytically reveal a simple property that holds for any two-strategy multiplayer games in well-mixed populations and on regular graphs: the evolutionary outcome in a population with heterogeneous update rules is the weighted average of the outcomes in the corresponding homogeneous populations, and the associated weights are the frequencies of each update rule in the heterogeneous population. Beyond weak selection, we show that this property holds for public goods games. Our finding implies that heterogeneous aspiration dynamics is additive. This additivity greatly reduces the complexity induced by the underlying individual heterogeneity. Our work thus provides an efficient method to calculate evolutionary outcomes under heterogeneous update rules.

During the last years, there has been a growing interest in the coupling between voltages and the magnetization of insulating nanostructures. Applied voltages can change the magnetic anisotropy of magnetic tunnel junctions and generate magnetization dynamics more efficiently than alternating magnetic fields and spin-polarized electric currents because it avoids the Joule dissipation. Here, we study the formation of dissipative breathers in nanomagnets forced by an oscillatory voltage. The breathers are localized states with an oscillatory envelope. The voltage frequency is close to twice the ferromagnetic resonance frequency. Numerical simulations reveal that the breathers can emit evanescent spin waves from their center in a dipolarlike shape when the voltage is above a certain threshold. Based on an amplitude equation, we explain the existence and behavior of these voltage-induced breathing solitons, while the anisotropic spin-wave emission corresponds to a spontaneous symmetry-breaking instability.

Dissipative vortices are stable two-dimensional localized structures existing due to balance between gain and loss in nonlinear systems far from equilibrium. Being resistant to the dispersion and nonlinear distortions they are considered as promising information carriers for new optical systems. The key challenge in the development of such systems is getting control over vortex waveforms. In this paper we report on replication of two-dimensional fundamental dissipative solitons and vortices due to their scattering on a locally applied potential in the cubic-quintic complex Ginzburg-Landau equation. It has been found that an appropriate potential nontrivially splits both fundamental solitons and vortices into a few exact copies without loss in their amplitude levels. A remarkably simple potential having a finite supporter along the longitudinal coordinate and a double-peaked dependence on a single-transverse coordinate is found to be suitable for the replication of the two-dimensional localized structures.

We introduce the phenomenon known as forced snaking to the study of gap solitons and use this notion to identify two distinct bifurcation diagrams organizing such solitons in the semi-infinite gap of the continuous cubic-quintic Gross-Pitaevskii equation with a spatially periodic potential. Standard snaking is found for small interpotential or lattice spacing while foliated snaking is present for large spacing. In each case, we determine the stability of the symmetric onsite and off-site solitons and show that multisoliton solutions of both types are stabilized when the spacing is sufficiently large, effectively quenching the interaction between the solitons. Finally, we show that the solitons unbind from the potential when subjected to sufficiently large asymmetric or symmetric perturbations and use direct numerical simulation to investigate their breakup and associated radiative losses as they propagate. A strongly nonlinear theory that captures key aspects of the depinning dynamics is provided.

Modeling the dynamics of an individual active particle invariably involves an isotropic noisy self-propulsion component, in the form of run-and-tumble motion or variations around it. This nonequilibrium source of noise is neither white—there is persistence—nor Gaussian. While emerging collective behavior in active matter has hitherto been attributed to the persistent ingredient, we focus on the non-Gaussian ingredient of self-propulsion. We show that by itself, that is, without invoking any memory effect, it is able to generate particle accumulation close to boundaries and effective attraction between otherwise repulsive particles, a mechanism which generically leads to motility-induced phase separation in active matter.

There is a rich diversity of surface topologies controllably engineered by patterning cavities embedded beneath the surface of soft materials. Upon external compression, the surface undergoes the reversible transformation from the flat surface to various surface topographies, including a periodic checkerboard pattern with alternate convex and concave features. To design the surface features, both two- (2D) and three-dimensional (3D) finite element based simulations are performed. It is demonstrated that the periodic surface features with controllable morphology, such as one-dimensional waves, checkerboard pattern, and mutually perpendicular apexes, etc., can be realized through varying cavity geometries (e.g., relative intercavity distance, shapes, and biaxial or uniaxial load). Additionally, a simple model for plate buckling is used to elucidate the effect of cavity aspect ratio on the surface pattern. Based on 3D printed prototypes, we further conduct experiments to validate the simulation results of 2D morphologies. The patterned cavities in soft materials make designing a variety of reversible surface features possible, offering an effective fabrication approach for wide application across multiple scales.