Relaxation time for a dimer covering with height representation

This paper considers the Monte Carlo dynamics of random dimer coverings of the square lattice, which can be mapped to a rough interface model. Two kinds of slow modes are identified, associated respectively with long-wavelength fluctuations of the interface height, and with slow drift (in time) of the system-wide mean height. Within a continuum theory, the longest relaxation time for either kind of mode scales as the system sizeN. For the real, discrete model, an exactlower bound ofO(N) is placed on the relaxation time, using variational eigenfunctions corresponding to the two kinds of continuum modes     

自对耦无序分布随机链Potts模型的临界普适性研究

以蒙特卡罗模拟方法对自对耦分布二维随机链q态Potts模型的短时临界行为进行了数值研究.利用初始非平衡演化阶段存在的普适幂指数和有限体积标度行为，数值模拟了在不同形式随机分布时q＝3和q＝8态Potts模型磁临界指数η和动力学临界指数z.计算结果发现η不依赖于自对偶无序分布的具体形式， 从而以数值方法给出了一个关于淬火掺杂自旋系统的临界普适行为的验证. 关键词： 随机链Potts模型 动力学蒙特卡罗模拟 临界普适性     

Finite-size effects at critical points with anisotropic correlations: Phenomenological scaling theory and Monte Carlo simulations

Various thermal equilibrium and nonequilibrium phase transitions exist where the correlation lengths in different lattice directions diverge with different exponentsv ,v : uniaxial Lifshitz points, the Kawasaki spin exchange model driven by an electric field, etc. An extension of finite-size scaling concepts to such anisotropic situations is proposed, including a discussion of (generalized) rectangular geometries, with linear dimensionL in the special direction and linear dimensionsL in all other directions. The related shape effects forL L but isotropic critical points are also discussed. Particular attention is paid to the case where the generalized hyperscaling relationv +(d–1)v =+2 does not hold. As a test of these ideas, a Monte Carlo simulation study for shape effects at isotropic critical point in the two-dimensional Ising model is presented, considering subsystems of a 1024x1024 square lattice at criticality.Visiting Supercomputer Senior Scientist at Rutgers University.     

Overcoming artificial spatial correlations in simulations of superstructure domain growth with parallel Monte Carlo algorithms

We study the applicability of parallelized/vectorized Monte Carlo (MC) algorithms to the simulation of domain growth in two-dimensional lattice gas models undergoing an ordering process after a rapid quench below an order-disorder transition temperature. As examples we consider models with 2×1 andc(2×2) equilibrium superstructures on the square and rectangular lattices, respectively. We also study the case of phase separation (1×1 islands) on the square lattice. A generalized parallel checkerboard algorithm for Kawasaki dynamics is shown to give rise to artificial spatial correlations in all three models. However, only ifsuperstructure domains evolve do these correlations modify the kinetics by influencing the nucleation process and result in a reduced growth exponent compared to the value from the conventional heat bath algorithm with random single-site updates. In order to overcome these artificial modifications, two MC algorithms with a reduced degree of parallelism (hybrid and mask algorithms, respectively) are presented and applied. As the results indicate, these algorithms are suitable for the simulation of superstructure domain growth on parallel/vector computers.     

Phase diagram of the Ising square lattice with competing interactions

We restudy the phase diagram of the 2D-Ising model with competing interactions J₁ on nearest neighbour and J₂ on next-nearest neighbour bonds via Monte-Carlo simulations. We present the finite temperature phase diagram and introduce computational methods which allow us to calculate transition temperatures close to the criticalpoint at J₂ = J₁/2. Further on we investigate the character of the different phase boundariesand find that the transition is weakly first order formoderate J₂ > J₁/2.     

Critical behavior of two-dimensional spin models and charge asymmetry in the Coulomb gas

Many two-dimensional spin models can be transformed into Coulomb-gas systems in which charges interact via logarithmic potentials. For some models, such as the eight-vertex model and the Ashkin-Teller model, the Coulomb-gas representation has added significantly to the insight in the phase transitions. For other models, notably theXY model and the clock models, the equivalence has been instrumental for almost our entire understanding of the critical behavior. Recently it was shown that theq-state Potts model and then-vector model are equivalent to a Coulomb gas with an asymmetry between positive and negative charges. Fieldlike operators in these spin models transform noninteger charges and magnetic monopoles. With the aid of exactly solved models the Coulombgas representation allows analytic calculation of some critical indices.