Phase transition and power-law coarsening in an Ising-doped voter model

On the renormalization group fixed point of the two-dimensional Ising model at criticality

We analyze the renormalization group fixed point of the two-dimensional Ising model at criticality. In contrast with expectations from tensor network renormalization (TNR), we show that a simple, explicit analytic description of this fixed point using operator-algebraic renormalization (OAR) is possible. Specifically, the fixed point is characterized in terms of spin-spin correlation functions. Explicit error bounds for the approximation of continuum correlation functions are given.

Fluctuation relations in a nonequilibrium system: Surface tension and effective temperature in an Ising-doped voter model

Fluctuation relations of Jarzynski and Crooks enable efficient calculations of a free-energy difference between equilibrium states. In the present paper, we provide some numerical evidence that these relations can also be used for a two-dimensional Ising-doped voter model, which is a nonequilibrium system with a violated detailed balance. Adopting the method of Híjar and Sutmann, we implement a protocol that switches between periodic and antiperiodic boundary conditions and induces formation of an interface in the model. Assuming that a suitably interpreted Ising Hamiltonian can be considered as a pseudoenergy of the model, we examine fluctuations of work performed during these processes and estimate the surface tension. Our results confirm that the surface tension remains positive in this model except a limiting case of the voter model, where it seems to vanish. Comparing the free-energy estimates at different speeds of the switching process, we also estimate an effective temperature in the model. Perhaps coincidentally, the effective temperature of the voter model appears to be close to the critical temperature of the Ising model.

Equilibrium behavior in a nonequilibrium system: Ising-doped voter model on complete graph

While the Ising model belongs to the realm of equilibrium statistical mechanics, the voter model is an example of a nonequilibrium system. We examine an opinion formation model, which is a mixture of Ising and voter agents with concentrations p and 1-p, respectively. Although in our model for p<1 a detailed balance is violated, on a complete graph the average magnetization in the stationary state for any p>0 is shown to satisfy the same equation as for the pure Ising model (p=1). Numerical simulations confirm such a behavior. Variance of magnetization and susceptibility in our model increase for decreasing p and diverge at the temperature at which magnetization vanishes. Simulations on a random graph also show that a small concentration of Ising agents is sufficient to induce a ferromagnetic ordering.

Big data-drive agent-based modeling of online polarized opinions

Under the mobile internet and big data era, more and more people are discussing and interacting online with each other. The forming process and evolutionary dynamics of public opinions online have been heavily investigated. Using agent-based modeling, we expand the Ising model to explore how individuals behave and the evolutionary mechanism of the life cycles. The big data platform of Douban.com is selected as the data source, and the online case “NeiYuanWaiFang” is applied as the real target, for our modeling and simulations to match. We run 10,000 simulations to find possible optimal solutions, and we run 10,000 times again to check the robustness and adaptability. The optimal solution simulations can reflect the whole life cycle process. In terms of different levels and indicators, the fitting or matching degrees achieve the highest levels. At the micro-level, the distributions of individual behaviors under real case and simulations are similar to each other, and they all follow normal distributions; at the middle-level, both discrete and continuous distributions of supportive and oppositive online comments are matched between real case and simulations; at the macro-level, the life cycle process (outbreak, rising, peak, and vanish) and durations can be well matched. Therefore, our model has properly seized the core mechanism of individual behaviors, and precisely simulated the evolutionary dynamics of online cases in reality.

Modeling and Analysis of Anomalies in the Network Infrastructure Based on the Potts Model

The paper discusses issues concerning the occurrence of anomalies affecting the process of phase transitions. The considered issue was examined from the perspective of phase transitions in network structures, particularly in IT networks, Internet of Things and Internet of Everything. The basis for the research was the Potts model in the context of IT networks. The author proposed the classification of anomalies in relation to the states of particular nodes in the network structure. Considered anomalies included homogeneous, heterogeneous, individual and cyclic disorders. The results of tests and simulations clearly showed the impact of anomalies on the phase transitions in the network structures. The obtained results can be applied in modelling the processes occurring in network structures, particularly in IT networks.

Evolution towards Linguistic Coherence in Naming Game With Migrating Agents

As an integral part of our culture and way of life, language is intricately related to the migrations of people. To understand whether and how migration shapes language formation processes, we examine the dynamics of the naming game with migrating agents. (i) When all agents may migrate, the dynamics generates effective surface tension that drives the coarsening. Such behaviour is very robust and appears for a wide range of densities of agents and their migration rates. (ii) However, when only multilingual agents are allowed to migrate, monolingual islands are typically formed. In such a case, when the migration rate is sufficiently large, the majority of agents acquire a common language that spontaneously emerges with no indication of surface-tension-driven coarsening. Relatively slow coarsening that takes place in a dense static population is very fragile, and an arbitrarily small migration rate can most likely divert the system towards the quick formation of monolingual islands. Our work shows that migration influences language formation processes, but additional details such as density or mobility of agents are needed to more precisely specify this influence.

Hurst entropy: A method to determine predictability in a binary series based on a fractal-related process

Shannon's concept of information is related to predictability. In a binary series, the value of information relies on the frequency of 0's and 1's, or how it is expected to occur. However, information entropy does not consider the bias in randomness related to autocorrelation. In fact, it is possible for a binary temporal series to carry both short- and long-term memories related to the sequential distribution of 0's and 1's. Although the Hurst exponent measures the range of autocorrelation, there is a lack of mathematical connection between information entropy and autocorrelation present in the series. To fill this important gap, we combined numerical simulations and an analytical approach to determine how information entropy changes according to the frequency of 0's and 1's and the Hurst exponent. Indeed, we were able to determine how predictability depends on both parameters. Our findings are certainly useful to several fields when binary times series are applied, such as neuroscience to econophysics.

Aging phenomena during phase separation in fluids: decay of autocorrelation for vapor-liquid transitions

We performed molecular dynamics simulations to study relaxation phenomena during vapor-liquid transitions in a single component Lennard-Jones system. Results from two different overall densities are presented: one in the neighborhood of the vapor branch of the coexistence curve and the other being close to the critical density. The nonequilibrium morphologies, growth mechanisms and growth laws in the two cases are vastly different. In the low density case growth occurs via diffusive coalescence of droplets in a disconnected morphology. On the other hand, the elongated structure in the higher density case grows via advective transport of particles inside the tube-like liquid domains. The objective in this work has been to identify how the decay of the order-parameter autocorrelation, an important quantity to understand aging dynamics, differs in the two cases. In the case of the disconnected morphology, we observe a very robust power-law decay, as a function of the ratio of the characteristic lengths at the observation time and at the age of the system, whereas the results for the percolating structure appear rather complex. To quantify the decay in the latter case, unlike the standard method followed in a previous study, here we have performed a finite-size scaling analysis. The outcome of this analysis shows the presence of a strong preasymptotic correction, while revealing that in this case also, albeit in the asymptotic limit, the decay follows a power-law. Even though the corresponding exponents in the two cases differ drastically, this study, combined with a few recent ones, suggests that power-law behavior of this correlation function is rather universal in coarsening dynamics.