arXiv subjects
Publications and source records attributed to J. F. Markham.
We use the Padé-Z$_2$ stochastic estimator for calculating Tr log M to compute quark loop corrections to quenched QCD. We examine the main source of error in this technique and look at a way of controlling it.
A simulation method based on the RG blocking is shown to yield statistical errors smaller than that of the crude MC using absolute values of the original measures. The new method is particularly suitable to apply to the sign problem of indefinite or complex-valued measures. We demonstrate the many advantages of this method in the simulation of 2D Ising model with complex-valued temperature.
Current algorithms used to put a lattice gauge configuration into Landau gauge either suffer from the problem of critical slowing-down or involve an additional computational expense to overcome it. Evolutionary Algorithms (EAs), which have been widely applied to other global optimisation problems, may be of use in gauge fixing. Also, being global, they should not suffer from critical slowing-down as do local gradient based algorithms. We apply EA's and also a Steepest Descent (SD) based method to the problem of Landau Gauge Fixing and compare their performance.
A method is proposed to handle the sign problem in the simulation of systems having indefinite or complex-valued measures. In general, this new approach, which is based on renormalisation blocking, is shown to yield statistical errors smaller than the crude Monte Carlo method using absolute values of the original measures. The improved method is applied to the 2D Ising model with temperature generalised to take on complex values. It is also adapted to implement Monte Carlo Renormalisation Group calculations of the magnetic and thermal critical exponents.
A simulation method based on the RG blocking is shown to yield statistical errors smaller than that of the crude MC using absolute values of the original measures. The new method is particularly suitable to apply to the sign problem of indefinite or complex-valued measures. We demonstrate the many advantages of this method in the simulation of 2D Ising model with complex-valued temperature.
The lattice fermion determinants, in a given background gauge field, are evaluated for two different kinds of random lattices and compared to those of naive and wilson fermions in the continuum limit. While the fermion doubling is confirmed on one kind of lattices, there is positive evidence that it may be absent for the other, at least for vector interactions in two dimensions. Combined with previous studies, arbitrary randomness by itself is shown to be not a sufficient condition to remove the fermion doublers.