Critical exponents of a three dimensional O(4) spin model

By Monte Carlo simulation we study the critical exponents governing the transition of the three-dimensional classical O(4) Heisenberg model, which is considered to be in the same universality class as the finite-temperature QCD with massless two flavors. We use the single cluster algorithm and the histogram reweighting technique to obtain observables at the critical temperature. After estimating an accurate value of the inverse critical temperature \Kc=0.9360(1), we make non-perturbative estimates for various critical exponents by finite-size scaling analysis. They are in excellent agreement with those obtained with the $4-\epsilon$ expansion method with errors reduced to about halves of them.Comment: 25 pages with 8 PS figures, LaTeX, UTHEP-28

Spin chain simulations with a meron cluster algorithm

We apply a meron cluster algorithm to the XY spin chain, which describes a quantum rotor. This is a multi-cluster simulation supplemented by an improved estimator, which deals with objects of half-integer topological charge. This method is powerful enough to provide precise results for the model with a theta-term - it is therefore one of the rare examples, where a system with a complex action can be solved numerically. In particular we measure the correlation length, as well as the topological and magnetic susceptibility. We discuss the algorithmic efficiency in view of the critical slowing down. Due to the excellent performance that we observe, it is strongly motivated to work on new applications of meron cluster algorithms in higher dimensions.Comment: 18 pages, 9 figures, published versio

Green's Functions from Quantum Cluster Algorithms

We show that cluster algorithms for quantum models have a meaning independent of the basis chosen to construct them. Using this idea, we propose a new method for measuring with little effort a whole class of Green's functions, once a cluster algorithm for the partition function has been constructed. To explain the idea, we consider the quantum XY model and compute its two point Green's function in various ways, showing that all of them are equivalent. We also provide numerical evidence confirming the analytic arguments. Similar techniques are applicable to other models. In particular, in the recently constructed quantum link models, the new technique allows us to construct improved estimators for Wilson loops and may lead to a very precise determination of the glueball spectrum.Comment: 15 pages, LaTeX, with four figures. Added preprint numbe

Universality in the Gross-Neveu model

We consider universal finite size effects in the large-N limit of the continuum Gross-Neveu model as well as in its discretized versions with Wilson and with staggered fermions. After extrapolation to zero lattice spacing the lattice results are compared to the continuum values.Comment: Lattice2004(theory

Ventilation times scales for a subtropical bay from 3-D modelling

[Abstract]: We applied a multi-purpose three-dimensional ocean general circulation model to compute water renewal time scales for a large coastal embayment situated off the central eastern coast of Australia (Hervey Bay) that shows features of an inverse estuary. Water renewal or ventilation time scales are not directly observable but can easily be diagnosed from numerical simulations. Improved knowledge of these time scales can assists in evaluating the water quality of coastal environments and can be utilised in sustainable marine resource management. The numerical studies are performed with the COupled Hydrodynamical Ecological model for REgioNal Shelf seas (COHERENS). The model, adopted for Hervey Bay, provided insight into ventilation pathways, and renewal time scales were found to exhibit a strong spatial variability. More than 80 % of the coastal embayment was fully ventilated after about 70-100 days, with the eastern and western shallow coastal regions ventilated more rapidly than the central, deeper part of the bay. The concept of a single ’typical’ ventilation timescale characterising this particular coastal embayment is inadequate and the consideration of spatial variability is clearly important, hence in a second set of simulations local monitoring boxes and Lagrangian tracers have been used to focus on this spatial variability. Simple parameters are derived to estimate local sedimentation, transport processes or places of high/low biological production

A Cluster Method for the Ashkin--Teller Model

A cluster Monte Carlo algorithm for the Ashkin-Teller (AT) model is constructed according to the guidelines of a general scheme for such algorithms. Its dynamical behaviour is tested for the square lattice AT model. We perform simulations on the line of critical points along which the exponents vary continuously, and find that critical slowing down is significantly reduced. We find continuous variation of the dynamical exponent $z$ along the line, following the variation of the ratio $\alpha/\nu$, in a manner which satisfies the Li-Sokal bound $z_{cluster}\geq\alpha/\nu$, that was so far proved only for Potts models.Comment: 18 pages, Revtex, figures include