An Agent-Based Statistical Physics Model for Political Polarization: A Monte Carlo Study.

World-wide, political polarization continues unabated, undermining collective decision-making ability. In this issue, we have examined polarization dynamics using a (mean-field) model borrowed from statistical physics, assuming that each individual interacted with each of the others. We use the model to generate scenarios of polarization trends in time in the USA and explore ways to reduce it, as measured by a polarization index that we propose. Here, we extend our work using a more realistic assumption that individuals interact only with "neighbors" (short-range interactions). We use agent-based Monte Carlo simulations to generate polarization scenarios, considering again three USA political groups: Democrats, Republicans, and Independents. We find that mean-field and Monte Carlo simulation results are quite similar. The model can be applied to other political systems with similar polarization dynamics.

Statistical Mechanics of Political Polarization.

Rapidly increasing political polarization threatens democracies around the world. Scholars from several disciplines are assessing and modeling polarization antecedents, processes, and consequences. Social systems are complex and networked. Their constant shifting hinders attempts to trace causes of observed trends, predict their consequences, or mitigate them. We propose an equivalent-neighbor model of polarization dynamics. Using statistical physics techniques, we generate anticipatory scenarios and examine whether leadership and/or external events alleviate or exacerbate polarization. We consider three highly polarized USA groups: Democrats, Republicans, and Independents. We assume that in each group, each individual has a political stance s ranging between left and right. We quantify the noise in this system as a "social temperature" T. Using energy E, we describe individuals' interactions in time within their own group and with individuals of the other groups. It depends on the stance s as well as on three intra-group and six inter-group coupling parameters. We compute the probability distributions of stances at any time using the Boltzmann probability weight exp(-E/T). We generate average group-stance scenarios in time and explore whether concerted interventions or unexpected shocks can alter them. The results inform on the perils of continuing the current polarization trends, as well as on possibilities of changing course.

Sociophysics Analysis of Multi-Group Conflicts.

We present our research on the application of statistical physics techniques to multi-group social conflicts. We identify real conflict situations of which the characteristics correspond to the model. We offer realistic assumptions about conflict behaviors that get factored into model-generated scenarios. The scenarios can inform conflict research and strategies for conflict management. We discuss model applications to two- and three-group conflicts. We identify chaotic time evolution of mean attitudes and the occurrence of strange attractors. We examine the role that the range of interactions plays with respect to the occurrence of chaotic behavior.

Skyrmions and Spin Waves in Magneto-Ferroelectric Superlattices.

We present in this paper the effects of Dzyaloshinskii-Moriya (DM) magneto-electric coupling between ferroelectric and magnetic interface atomic layers in a superlattice formed by alternate magnetic and ferroelectric films. We consider two cases: magnetic and ferroelectric films have the simple cubic lattice and the triangular lattice. In the two cases, magnetic films have Heisenberg spins interacting with each other via an exchange J and a DM interaction with the ferroelectric interface. The electrical polarizations of ±1 are assumed for the ferroelectric films. We determine the ground-state (GS) spin configuration in the magnetic film and study the phase transition in each case. In the simple cubic lattice case, in zero field, the GS is periodically non collinear (helical structure) and in an applied field H perpendicular to the layers, it shows the existence of skyrmions at the interface. Using the Green's function method we study the spin waves (SW) excited in a monolayer and also in a bilayer sandwiched between ferroelectric films, in zero field. We show that the DM interaction strongly affects the long-wave length SW mode. We calculate also the magnetization at low temperatures. We use next Monte Carlo simulations to calculate various physical quantities at finite temperatures such as the critical temperature, the layer magnetization and the layer polarization, as functions of the magneto-electric DM coupling and the applied magnetic field. Phase transition to the disordered phase is studied. In the case of the triangular lattice, we show the formation of skyrmions even in zero field and a skyrmion crystal in an applied field when the interface coupling between the ferroelectric film and the ferromagnetic film is rather strong. The skyrmion crystal is stable in a large region of the external magnetic field. The phase transition is studied.

Statistical Physics Approach to Liquid Crystals: Dynamics of Mobile Potts Model Leading to Smectic Phase, Phase Transition by Wang-Landau Method.

We study the nature of the smectic-isotropic phase transition using a mobile 6-state Potts model. Each Potts state represents a molecular orientation. We show that with the choice of an appropriate microscopic Hamiltonian describing the interaction between individual molecules modeled by a mobile 6-state Potts spins, we observe the smectic phase dynamically formed when we cool the molecules from the isotropic phase to low temperatures (T). In order to elucidate the order of the transition and the low-T properties, we use the high-performance Wang-Landau flat energy-histogram technique. We show that the smectic phase goes to the liquid (isotropic) phase by melting/evaporating layer by layer starting from the film surface with increasing T. At a higher T, the whole remaining layers become orientationally disordered. The melting of each layer is characterized by a peak of the specific heat. Such a succession of partial transitions cannot be seen by the Metropolis algorithm. The successive layer meltings/evaporations at low T are found to have a first-order character by examining the energy histogram. These results are in agreement with experiments performed on some smectic liquid crystals.

Phase Transition in Frustrated Magnetic Thin Film-Physics at Phase Boundaries.

In this review, we outline some principal theoretical knowledge of the properties of frustrated spin systems and magnetic thin films. The two points we would like to emphasize: (i) the physics in low dimensions where exact solutions can be obtained; (ii) the physics at phase boundaries where interesting phenomena can occur due to competing interactions of the two phases around the boundary. This competition causes a frustration. We will concentrate our attention on magnetic thin films and phenomena occurring near the boundary of two phases of different symmetries. Two-dimensional (2D) systems are in fact the limiting case of thin films with a monolayer. Naturally, we will treat this case at the beginning. We begin by defining the frustration and giving examples of frustrated 2D Ising systems that we can exactly solve by transforming them into vertex models. We will show that these simple systems already contain most of the striking features of frustrated systems such as the high degeneracy of the ground state (GS), many phases in the GS phase diagram in the space of interaction parameters, the reentrance occurring near the boundaries of these phases, the disorder lines in the paramagnetic phase, and the partial disorder coexisting with the order at equilibrium. Thin films are then presented with different aspects: surface elementary excitations (surface spin waves), surface phase transition, and criticality. Several examples are shown and discussed. New results on skyrmions in thin films and superlattices are also displayed. By the examples presented in this review we show that the frustration when combined with the surface effect in low dimensions gives rise to striking phenomena observed in particular near the phase boundaries.