D. L. Hunter

The dynamic critical exponent of the three-dimensional Ising model

We measure the dynamic exponent of the three-dimensional Ising model using a “damage spreading” Monte Carlo approach as described by MacIsaac and Jan. We simulate systems fromL=5 toL=60 at the critical temperature,Tc=4.5115. We report a dynamic exponent,z=2.35±0.05, a value much larger than the “consensus” value of 2.02, whereas if we assume logarithmic corrections, we find thatz=2.05±0.05.

SPECIATION FROM EVOLUTION

Evolution, based on the principles of mutation and selection, is a powerful basis for microscopic changes which can account for the evolution of a species and macroscopic speciation where there is splitting of a species into two distinct new species. We show that a single species evolves into distinct species after several generations in an unrestricted genome space.

Influence Of Boundary Conditions On The Fraction Of Spanning Clusters

We use the Hoshen–Kopelman algorithm with the Nakanashi method of recycling redundant labels to measure the fraction of spanning configurations, R(pc), at and near pc, for random site percolation in two and three dimensions with different boundary conditions. For the square and cubic lattices we find that R(pc) is 0.50 and 0.28 for free edges and 0.64 (2-d) and 0.56 (3-d) for both helical and periodic boundary conditions. The error bars are of the order of ±0.01 for these results.

Time-dependent critical properties of Ising models by damage spreading

We use the method of damage spreading to study the time, t, taken for a spin at a distance r to be damaged for the first time in Ising models with heat-bath dynamics. We report time-dependent scaling exponents, dt ≃ 2.0 (1D), 2.52 (2D), 2.26 (3D) and (2.0) (4D), if we assume that t ∾ rdt. We also analyze our data assuming various forms of logarithmic corrections and we find that dt ∾ 2.25 or less (2D) and ∾2.0 (3D). We argue that it is extremely plausible that dt is equal to z, the dynamic critical exponent, and thus our estimate of z, in two dimensions is higher than the “consensus” value of 2.14, but we find good agreement in one, three and four dimensions with the exact and expected values.

Evolution of hunter–gatherer strategies with a genetically inspired algorithm

We address the following: Are there several optimal strategies for a hunter-gatherer society in a given environment, in which the society has an evolving level of technology and/or skills? We use the Genetic Algorithm, with point mutations, to facilitate the search for these strategies. We find that, in a generous environment, several optimal strategies are possible; there is no unique optimal strategy. We are now in a position, with the Genetic Algorithm, to assess different approaches to resource exploitation and the role of contingency.

Local equilibrium Monte Carlo simulations

Abstract We study the evolution of the Ising model in non-equilibrium situations but with the assumption that local equilibrium is possible. The time scale is such that there is a well defined local temperature which may be different from the average or equilibrium temperature. We apply the Metropolis algorithm to determine the behaviour of the spins in such an environment. Two special cases are considered: (i) the system evolving in a temperature gradient and (ii) a sudden quench from a high temperature to low temperature. In both cases the dissipation of heat to the thermal reservoirs is taken into account.