Ising Spin Variables Research Articles

DYNAMICAL PHASE TRANSITIONS IN OPINION NETWORKS: COEXISTENCE OF OPPORTUNISTS AND CONTRARIANS

We study a model for the emergence of collective decision making, consisting of N interacting agents, whose opinions are described by Ising spin variables. In particular, we present dynamical phase transitions from ordered to chaotic behavior in the space-time evolution of the binary choice network. One focus of this study is the determination of critical parameters, where the network is placed “at the edge of chaos,” i.e., at a subtle compromise between stability and flexibility, where the system has both, the necessary stability and the potential for “evolutionary” improvements.

Memory effects of the multi-charge network model

We propose a spin glass model which has interactions characterized by P kinds of charges carried by N kinds of particles. When the densities of the particles are assumed to be Ising spin variables, this model becomes a spin glass model which has an opposite interactional sign to the Hopfield model with P memorized patterns. The number of local minimum states and remanent magnetization are studied to clarify the memory effects of the model. We find that, as P/ N decreases, both quantities tend to the maximum possible values of the thermodynamic limit.

A Spin Model for Clustering of Amphiphiles in Two Dimensions

In this work we studied a simple spin-1 model to account for the aggregation properties observed in dilute amphiphilic solutions. We mapped the water and amphiphilic molecules by Ising spin variables with S = 1 . The zero component of the spin S is used to describe the water molecules, while the two other components (±1) account for the amphiphiles. We performed Monte Carlo simulations for two-dimensional lattices employing Glauber single spin-flip and a Kawasaki double spin-exchange dynamics. The energy is given by the usual —JSiSj exchange term and by a contribution in the form —DS2iS2j. In the limit of very low concentration of amphiphiles, we observed the so-called critical micellar concentration; however, the aggregate distribution curve does not exhibit the local minimum and maximum characteristic of the micellar solution for all values of the parameters D and J. Finally, the model is exactly soluble in one dimension and compared with our two-dimensional numerical calculations.

Spin-1 aggregation model in one dimension

We studied a simple model of aggregation in one dimension that resembles the self-assembly of amphiphiles in an aqueous solution. We mapped the water and amphiphilic molecules by Ising spin variables for S=1. The zero component of spin represents the water molecules, while the remaining components (+/-1) account for the amphiphilic molecules. We defined an aggregate in one dimension by a set of spin components (+/-1) placed between two zero spin components. There is no difference between up and down components of the spins inside the aggregates. In this way what really matters is the square of the spin component. The grand-canonical partition function and the probability of formation of different aggregate sizes were calculated by the transfer matrix method. We have shown that for any value of the chemical potential and temperature, the system does not exhibit the typical aggregate size distribution which is observed in micellar solutions at low concentrations. The distribution curve for the aggregate size does not show the minimum and the maximum as a function of the concentration which is the signature of the appearance of micelles. We can say that this one-dimensional model does not present any phase transition nor a transition from the micellar to nonmicellar state.

Path-integral theory for light-absorption spectra of many-electron systems in insulating states due to strong long-range Coulomb repulsion: Nonlinear coupling between charge and spin excitations

We develop a path-integral formulation which is free from Grassmann algebras to calculate absorption spectra of strongly correlated electron systems. The Coulomb repulsions, including not only the short-range part but also a long-range part, are reduced into a time-dependent one-body Hamiltonian with only two kinds of Ising spin variables per site. The sums over these spin configurations are performed according to the quantum Monte Carlo techniques. By this method we disclose the electron correlation effects on absorption spectra. The method is applied to the one-dimensional half-filled electron systems, where the ground state is an insulating state due to the strong long-range Coulomb repulsion and contains large quantum fluctuations by low-energy collective spin excitations. The absorption spectrum shows an infrared divergencelike structure, which seems to arise from the simultaneous excitation of the charge-transfer exciton and collective spin excitations. The spectrum also contains new peaks on the high energy side which correspond to the multiple excitation of electron-hole pairs. Such a multiple excitation is caused by the electron correlation effect, through which the photogenerated electron and hole can excite other electron-hole pairs. Our result clearly shows that charge and spin of the electron are inseparable in a many-body system in an insulating state caused by the strong long-range Coulomb repulsion.

Computer Simulation of Liquid Wetting Dynamics in Fiber Structures Using the Ising Model

We present in this paper a method which applies the so-called Ising model and Kawasaki thermodynamics, combined with the Monte Carlo computer simulation technique to study the liquid-fiber interaction and the wetting behavior of fiber networks. The various types of interactions occurring during a wetting process in a fiber mass are analyzed, and their individual contributions towards the Hamiltonian system are derived. The criterion for energy state exchange between the Ising spin variables is given as the critical step for the wetting simulation. The procedures of the simulation algorithm are provided. Various predictions of the wetting process including wetting of a fiber network, the spreading of a liquid drop on a single fiber as well as a brief parametric study are included in this paper.

Many Commensurate Phases of a One-Dimensional Systemof Hard-Core Particles with Ising Spin Variables

We introduce a new one-dimensional competitive system constructed of particles with Ising spin variables in a periodic substrate potentials, a hard-core type inter-particle interaction and a spin-spin interaction whose exchange energy depends linearly on the distance between adjacent particles. The hard-core interaction mediates an antiferromagnetic spin-spin interaction. Although the range of the inter-particle interaction is finite, long-period commensurate phases are caused. Many commensurate phases appear in the ground state phase diagram.

Theory of ocular dominance column formation

A general theory previously proposed by the author which describes synaptic stabilization on the basis of three basic assumptions is employed for the understanding of ocular dominance column formation. A reduced mathematical model is constructed based on the thermodynamics in the Ising spin variables representing the afferent synaptic connection distribution. The results of Monte Carlo simulations on the segregation of ipsilateral and contralateral synaptic terminals in the input layer of the primary visual cortex suggest the existence of phase transition phenomena. Three types of ocular dominance column patterns--stripe, blob, and uniform--are visualized according to the values of the correlation strength and the degree of imbalance in activity between the left and right retinas. The theory presented here successfully explains how ocular dominance columns are developed.

The Ising spin partition function for the U=∞ Anderson model

It is shown how auxiliary Ising spin variables can be introduced to eliminate the fermion degrees of freedom in the partition function for the constrained U= infinity single impurity Anderson model. This allows the use of conventional Monte Carlo methods to calculate numerically static correlation functions.

Possibility of the Kosterlitz-Thouless Phase Transition in the Two Dimensional Fully Frustrated Ising Model

Fully frustrated Ising models on two-dimensional lattice with the first and second or third nearest neighbor interactions are studied. Original Ising spin variables are transformed into the cell spin variables, whose Hamiltonian is derived. The interaction of states and the role of excited states are discussed. Order parameters of the fully frustrated systems are proposed in a unified way. Vortex and antivortex excitations are observed by Monte Carlo simulation. Results strongly predict the Kosterlitz-Thouless phase transition in the model.