Advanced Dynamic Algorithms for the Decay of Metastable Phases in Discrete Spin Models: Bridging Disparate Time Scales

An overview of advanced dynamical algorithms capable of spanning the widely disparate time scales that govern the decay of metastable phases in discrete spin models is presented. The algorithms discussed include constrained transfer-matrix, Monte Carlo with Absorbing Markov Chains (MCAMC), and projective dynamics (PD) methods. The strengths and weaknesses of each of these algorithms are discussed, with particular emphasis on identifying the parameter regimes (system size, temperature, and field) in which each algorithm works best.Comment: 12 pages, 4 figures, proceedings of the US-Japan bilateral seminar on `Understanding and Conquering Long Time Scales in Computer Simulations', July 1999, to appear in Int. J. Mod. Phys.

A Tutorial on Advanced Dynamic Monte Carlo Methods for Systems with Discrete State Spaces

Advanced algorithms are necessary to obtain faster-than-real-time dynamic simulations in a number of different physical problems that are characterized by widely disparate time scales. Recent advanced dynamic Monte Carlo algorithms that preserve the dynamics of the model are described. These include the $n$-fold way algorithm, the Monte Carlo with Absorbing Markov Chains (MCAMC) algorithm, and the Projective Dynamics (PD) algorithm. To demonstrate the use of these algorithms, they are applied to some simplified models of dynamic physical systems. The models studied include a model for ion motion through a pore such as a biological ion channel and the metastable decay of the ferromagnetic Ising model. Non-trivial parallelization issues for these dynamic algorithms, which are in the class of parallel discrete event simulations, are discussed. Efforts are made to keep the article at an elementary level by concentrating on a simple model in each case that illustrates the use of the advanced dynamic Monte Carlo algorithm.Comment: 53 pages, 17 figure

Dispersive Approach to Chiral Perturbation Theory

We generalise the reconstruction theorem of Stern, Sazdjian, and Fuchs based on the dispersion relations to the case of the (2 -> 2) scattering of all the pseudoscalar octet mesons (pi, K, eta). We formulate it in a general way and include also a discussion of the assumptions of the theorem. It is used to obtain the amplitudes of all such processes in the isospin limit to the one-loop order (and can be straightforwardly extended to two loops) independently on the particular power-counting scheme of the chiral perturbation theory in question. The results in this general form are presented.Comment: 25 pages, 1 figure; added one appendix and correction of typo

On the Possibility of Quasi Small-World Nanomaterials

The possibility of materials that are governed by a fixed point related to small world networks is discussed. In particular, large-scale Monte Carlo simulations are performed on Ising ferromagnetic models on two different small-world networks generated from a one-dimensional spin chain. One has the small-world bond strengths independent of the length, and exhibits a finite-temperature phase transition. The other has small-world bonds built from atoms, and although there is no finite-temperature phase transition the system shows a slow power-law change of the effective critical temperature of a finite system as a function of the system size. An outline of a possible synthesis route for quasi small-world nanomaterials is presented.Comment: 13 pages, 9 figures, submitted to Brazilian Journal of Physics, conference proceedings for III Brazilian Meeting on Simulational Physics (2003

Monte Carlo Renormalization Group Study of the d=1 XXZ Model

We report current progress on the synthesis of methods to alleviate two major difficulties in implementing a Monte Carlo Renormalization Group (MCRG) for quantum systems. In particular, we have utilized the loop-algorithm to reduce critical slowing down, and we have implemented an MCRG method in which the symmetries of the classical equivalent model need not be fully understood, since the Renormalization Group is given by the Monte Carlo simulation. We report preliminary results obtained when the resulting MCRG method is applied to the d=1 XXZ model. Our results are encouraging. However, since this model has a Kosterlitz-Thouless transition, it does not yet provide a full test of our MCRG method.Comment: To appear in "Quantum Monte Carlo Methods in Condensed Matter Physics", ed.\ M. Suzuki, World Scientific, 1993. 14 pages, LaTeX, (3 figures available on request), FSU-SCRI-93-11