B. Zheng

Monte Carlo Simulations of Short-Time Critical Dynamics

The short-time behaviour of the critical dynamics for magnetic systems is investigated with Monte Carlo methods. Without losing the generality, we consider the relaxation process for the two dimensional Ising and Potts model starting from an initial state with very high temperature and arbitrary magnetization. We confirm the generalized scaling form and observe that the critical characteristic functions of the initial magnetization for the Ising and the Potts model are quite different.

Cross-correlation in financial dynamics

To investigate the universal structure of interactions in financial dynamics, we analyze the cross-correlation matrix C of price returns of the Chinese stock market, in comparison with those of the American and Indian stock markets. As an important emerging market, the Chinese market exhibits much stronger correlations than the developed markets. In the Chinese market, the interactions between the stocks in a same business sector are weak, while extra interactions in unusual sectors are detected. Using a variation of the two-factor model, we simulate the interactions in financial markets.

Networking effects on cooperation in evolutionary snowdrift game

The effects of networking on the extent of cooperation emerging in a competitive setting are studied. The evolutionary snowdrift game, which represents a realistic alternative to the well-known Prisoners Dilemma game, is studied in the Watts-Strogatz network that spans the regular, small-world, and random networks through random re-wiring. Over a wide range of payoffs, a re-wired network is found to suppress cooperation when compared with a well-mixed system. Two extinction payoffs, that characterize the emergence of a homogeneous steady state, are identified. It is found that, unlike in the Prisoners Dilemma game, the standard deviation of the degree distribution is the dominant network property that governs the extinction payoffs.

Weighted scale-free networks with stochastic weight assignments.

We propose a model of weighted scale-free networks incorporating a stochastic scheme for weight assignments to the links, taking into account both the popularity and fitness of a node. As the network grows, the weights of links are driven either by the connectivity with probability p or by the fitness with probability 1-p. Numerical results show that the total weight exhibits a power-law distribution with an exponent sigma that depends on the probability p. The exponent sigma decreases continuously as p increases. For p=0, the scaling behavior is the same as that of the connectivity distribution. An analytical expression for the total weight is derived so as to explain the features observed in the numerical results. Numerical results are also presented for a generalized model with a fitness-dependent link formation mechanism.

Dynamic Monte Carlo Measurement of Critical Exponents.

Based on the scaling relation for the dynamics at the early time, a new method is proposed to measure both the static and dynamic critical exponents. The method is applied to the two dimensional Ising model. The results are in good agreement with the existing results. Since the measurement is carried out in the initial stage of the relaxation process starting from independent initial configurations, our method is efficient.

Financial networks with static and dynamic thresholds

Based on the daily data of American and Chinese stock markets, the dynamic behavior of a financial network with static and dynamic thresholds is investigated. Compared with the static threshold, the dynamic threshold suppresses the large fluctuation induced by the cross-correlation of individual stock prices, and leads to a stable topological structure in the dynamic evolution. Long-range time-correlations are revealed for the average clustering coefficient, average degree and cross-correlation of degrees. The dynamic network shows a two-peak behavior in the degree distribution.

DYNAMIC APPROACH TO THE FULLY FRUSTRATED XY MODEL

Using Monte Carlo simulations, we systematically investigate the nonequilibrium dynamics of the chiral degree of freedom in the two-dimensional fully frustrated XY model. By means of the short-time dynamics approach, we estimate the second order phase transition temperature Tc and all the dynamic and static critical exponents u, z, b, and n. [S0031-9007(98)06479-5] PACS numbers: 75.10.Hk, 64.60.Cn, 64.60.Ht, 75.40.Mg For critical phenomena, it is traditionally believed that universal behavior exists only in equilibrium or in the longtime regime of the dynamical evolution. The universal scaling behavior is described by a number of critical exponents. Because of critical slowing down, numerical measurements of the critical exponents are very difficult. Recently, much progress has been achieved in dynamic critical phenomena. It was discovered that, already after a microscopic time scale tmic, universal scaling behavior emerges in the macroscopic short-time regime of the dynamic process [1‐6]. We first consider the following dynamic relaxation process: a magnetic system initially in a high-temperature state with a small initial magnetization m0 is quenched to the critical temperature Tc without an external magnetic field and then released to dynamic evolution of model A. The dynamics of model A is a relaxiational dynamics without conservation of energy and order parameter [7]. At the onset of the evolution, the magnetization is subjected to the scaling form [1,4,5,8,9]

THE SHORT-TIME DYNAMICS OF THE CRITICAL POTTS MODEL

Abstract The universal behaviour of the short-time dynamics of the three state Potts model in two dimensions at criticality is investigated with Monte Carlo methods. The initial increase of the order is observed. The new dynamic exponent θ as well as the exponent z and β ν are determined. The measurements are carried out in the very beginning of the time evolution. The spatial correlation length is found to be very short compared with the lattice size.

Anti-correlation and subsector structure in financial systems

With the random matrix theory, we study the spatial structure of the Chinese stock market, the American stock market and global market indices. After taking into account the signs of the components in the eigenvectors of the cross-correlation matrix, we detect the subsector structure of the financial systems. The positive and negative subsectors are anti-correlated with respect to each other in the corresponding eigenmode. The subsector structure is strong in the Chinese stock market, while somewhat weaker in the American stock market and global market indices. Characteristics of the subsector structures in different markets are revealed.

FINITE-SIZE SCALING AND CRITICAL EXPONENTS IN CRITICAL RELAXATION

We simulate the critical relaxation process of the two-dimensional Ising model with the initial state both completely disordered or completely ordered. Results of a new method to measure both the dynamic and static critical exponents are reported, based on the finite size scaling for the dynamics at the early time. From the time-dependent Binder cumulant, the dynamical exponent