Systematic errors due to linear congruential random-number generators with the Swendsen-Wang algorithm: A warning

We show that linear congruential pseudo-random-number generators can cause systematic errors in Monte Carlo simulations using the Swendsen-Wang algorithm, if the lattice size is a multiple of a very large power of 2 and one random number is used per bond. These systematic errors arise from correlations within a single bond-update half-sweep. The errors can be eliminated (or at least radically reduced) by updating the bonds in a random order or in an aperiodic manner. It also helps to use a generator of large modulus (e.g. 60 or more bits).Comment: Revtex4, 4 page

Grassmann Integral Representation for Spanning Hyperforests

Given a hypergraph G, we introduce a Grassmann algebra over the vertex set, and show that a class of Grassmann integrals permits an expansion in terms of spanning hyperforests. Special cases provide the generating functions for rooted and unrooted spanning (hyper)forests and spanning (hyper)trees. All these results are generalizations of Kirchhoff's matrix-tree theorem. Furthermore, we show that the class of integrals describing unrooted spanning (hyper)forests is induced by a theory with an underlying OSP(1|2) supersymmetry.Comment: 50 pages, it uses some latex macros. Accepted for publication on J. Phys.

Application of the O(N)O(N)-Hyperspherical Harmonics to the Study of the Continuum Limits of One-Dimensional σ\sigma-Models and to the Generation of High-Temperature Expansions in Higher Dimensions

In this talk we present the exact solution of the most general one-dimensional $O(N)$-invariant spin model taking values in the sphere $S^{N-1}$, with nearest-neighbour interactions, and we discuss the possible continuum limits. All these results are obtained using a high-temperature expansion in terms of hyperspherical harmonics. Applications in higher dimensions of the same technique are then discussed.Comment: 59208 bytes uuencoded gzip'ed (expands to 135067 bytes Postscript); 4 pages including all figures; contribution to Lattice '9

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

Failure of vaccination to prevent outbreaks of foot-and-mouth disease

Outbreaks of foot-and-mouth disease persist in dairy cattle herds in Saudi Arabia despite revaccination at intervals of 4-6 months. Vaccine trials provide data on antibody responses following vaccination. Using this information we developed a mathematical model of the decay of protective antibodies with which we estimated the fraction of susceptible animals at a given time after vaccination. The model describes the data well, suggesting over 95% take with an antibody half-life of 43 days. Farm records provided data on the time course of five outbreaks. We applied a 'SLIR' epidemiological model to these data, fitting a single parameter representing disease transmission rate. The analysis provides estimates of the basic reproduction number R(0), which may exceed 70 in some cases. We conclude that the critical intervaccination interval which would provide herd immunity against FMDV is unrealistically short, especially for heterologous challenge. We suggest that it may not be possible to prevent foot-and-mouth disease outbreaks on these farms using currently available vaccines

Abstract cluster expansion with applications to statistical mechanical systems

We formulate a general setting for the cluster expansion method and we discuss sufficient criteria for its convergence. We apply the results to systems of classical and quantum particles with stable interactions