Impact of the topology of global macroeconomic network on the spreading of economic crises.

Throughout economic history, the global economy has experienced recurring crises. The persistent recurrence of such economic crises calls for an understanding of their generic features rather than treating them as singular events. The global economic system is a highly complex system and can best be viewed in terms of a network of interacting macroeconomic agents. In this regard, from the perspective of collective network dynamics, here we explore how the topology of the global macroeconomic network affects the patterns of spreading of economic crises. Using a simple toy model of crisis spreading, we demonstrate that an individual country's role in crisis spreading is not only dependent on its gross macroeconomic capacities, but also on its local and global connectivity profile in the context of the world economic network. We find that on one hand clustering of weak links at the regional scale can significantly aggravate the spread of crises, but on the other hand the current network structure at the global scale harbors higher tolerance of extreme crises compared to more "globalized" random networks. These results suggest that there can be a potential hidden cost in the ongoing globalization movement towards establishing less-constrained, trans-regional economic links between countries, by increasing vulnerability of the global economic system to extreme crises.

Scaling exponents and transition behavior of the generalized conserved lattice gas model at zero temperature.

We study a generalized conserved lattice gas model in two dimensions by introducing an effective temperature to the conserved lattice gas model, where the number of particles is conserved during the dynamical process. We apply Monte Carlo simulation with the Metropolis transition rate. At zero temperature we find two transition behaviors; one between the localized active states and absorbing states and the other between the localized active states and active states. With a different definition of the order parameter for the second transition behavior, we obtain the critical exponents at the transition point.

Existence of an upper critical dimension in the majority voter model.

We study the critical properties of the majority voter model on d -dimensional hypercubic lattices. In two dimensions, the majority voter model belongs to the same universality class as that of the Ising model. However, the critical behaviors of the majority voter model on four dimensions do not exhibit mean-field behavior. Using the Monte Carlo simulation on d -dimensional hypercubic lattices, we obtain the critical exponents up to d=7 , and find that the upper critical dimension is 6 for the majority voter model. We also confirm our results using mean-field calculation.

Critical behavior of the majority voter model is independent of transition rates.

We study the critical properties of the majority voter model by using two different transition rates: the Glauber rate and the Metropolis rate. The model with the Glauber rate has been found to be mapped to the majority voter model with noise [de Oliveira, J. Stat. Phys. 66, 273 (1992)]. The critical temperature and the critical exponents for the two transition rates are obtained from a Monte Carlo simulation with a finite size scaling analysis. The critical temperature is found to depend on the transition rate, but the critical exponents do not. The values of the critical exponents obtained indicate that the model belongs to the same universality class as the Ising model, regardless of the type of transition rate.

Critical behavior of the XY model on growing scale-free networks.

Applying the histogram reweighting method, we investigate the critical behavior of the XY model on growing scale-free networks with various degree exponents lambda. For lambda < or = 3 , the critical temperature diverges as it does for the Ising model on scale-free networks. For lambda=8 , on the other hand, we observe a second-order phase transition at finite temperature. We obtain the critical temperature T{c}=3.08(2) and the critical exponents nu=2.62(3) , gammanu=0.127(4) , and betanu=0.442(2) from a finite-size scaling analysis.

Sub-block order parameter in a driven Ising lattice gas using block distribution functions.

We investigate the order parameter of the standard Ising lattice gas and driven Ising lattice gas models. The sub-block order parameter is introduced to these conserved models as an order parameter using block distribution functions. We also introduce the sub-block order parameter of damage using the block distribution functions of damage. We measure the sub-block order parameters using the Metropolis and heat-bath rates. These order parameters work well for the non-equilibrium-conserved model as well as the equilibrium-conserved model. We obtain the critical exponent of order parameter beta=1/8 for the standard Ising lattice gas and beta=1/2 for a driven Ising lattice gas using the Metropolis and heat-bath rates.

Absorbing phase transition with a conserved field.

We study a lattice gas model where the number of particles is conserved during dynamical process. Our model shows a continuous phase transition from a fluctuating phase to two symmetric absorbing states at the critical point in one dimension. We conjecture the values of the critical exponents characterizing the phase transition of our model. We show that the obtained values are in good agreement with those estimated from computer simulations. The critical exponents indicate that our model exhibits an absorbing phase transition which is different from the known ones.

Growth of a tensionless interface in anisotropic random media.

We introduce a simple growth model where a tensionless interface grows in random media. In this model, the degree of anisotropy of the random media is controlled by a variable g. When g=0, there is no anisotropic property of the random media. But, the anisotropic property increases as g does from 0. From the numerical simulations, we find that this model belongs to the quenched Herring-Mullins universality class when g=0. Interestingly, however, we find that this model belongs to the quenched Kardar-Parisi-Zhang universality class when g is nonzero.

Transition from stable to unstable growth by an inertial force.

We introduce a simple growth model where the growth of the interface is affected by an inertial force and a white noise. The magnitude of the inertial force is controlled by a constant p between 0 and 1. An inertial force increases continuously from 0, as p does from 0 to 1. In our model, the interface starts growing from a flat state. When pp(c), however, the interface width increases continuously without saturation as time elapses. We explain via simple calculation how this interesting phenomenon occurs in our model. We find p(c)=0.5 from the calculation. This critical value is in excellent agreement with the critical value p(c)=0.50(1) found from the simulations of our model.

Self-organized interface growth with the negative nonlinearity in a random medium.

We introduce two self-organized growth models that describe the motion of the driven interfaces in random media including the Kardar-Parisi-Zhang (KPZ) nonlinearity. One model follows the quenched KPZ equation with a positive nonlinear term, while the other model follows the quenched KPZ equation with a negative nonlinear term. By obtaining the critical exponents for two models, we confirm that the sign of the KPZ nonlinear term does not affect the universality class.

Phase transition in a triplet process.

We argue that the reaction-diffusion process 3A-->4A,3A-->2A exhibits a different type of continuous phase transition from an active into an absorbing phase. Because of the upper critical dimension d(c)> or =4/3 we expect the phase transition in 1+1 dimensions to be characterized by nontrivial fluctuation effects.

Well-defined set of exponents for a pair contact process with diffusion.

Recently it was suggested that a pair contact process with diffusion (PCPD) might represent an independent new universality class different from the directed percolation (DP) and the parity conservation (PC) class. The dynamics in the PCPD are usually controlled by two independent parameters. The critical exponents for the PCPD are known to have different values for varying values of the two independent parameters. However, once the diffusion and annihilation (or coagulation) rate in the PCPD is tuned in a way that the process without offspring production is exactly solvable, a well-defined set of the exponents for the PCPD is obtained. Then dynamics are controlled by only one independent parameter. The obtained critical exponents are different than those of DP and PC. The critical exponents satisfy the generalized hyperscaling relation within numerical errors.

First-order transition in a particle deposition-evaporation model.

We introduce a simple stochastic growth model where particles of two different species are deposited and evaporated. In the model, a randomly chosen particle of two species is deposited at a rate p and a particle on the edge of the plateau of the interface is evaporated at a rate 1-p. When pp(c2)=0.5015(5), the velocity of the interface is zero. When p(c1)

Stochastic growth models for driven interfaces through random media in two and three dimensions.

We introduce two simple stochastic growth models which describe the motion of the interfaces driven through random media in two and three dimensions. One model describes the motion of the interface driven through isotropic random media, where the dynamics of the interface can be described by the quenched Edwards-Wilkinson (QEW) equation. The other model describes the motion of the interface driven through anisotropic random media, where the dynamics of the interface can be described by the quenched Kardar-Parisi-Zhang (QKPZ) equation. We show via computer simulations that two models belong to the QEW and QKPZ universality class in two and three dimensions, respectively.