Improved Monte Carlo Method Research Articles

Two-dimensional polymers: universality and correction to scaling

Improved Monte Carlo methods have been used to study the asymptotic behaviour of self-avoiding walks on two-dimensional lattices. The mean-square end-to-end distance RN2 and radius of gyration SN2 are both found to scale as N2v with exponent values very close to the expected v=3/4 and an amplitude ratio that is universal. Small-N deviations of RN2 from the asymptotic results indicate a correction to scaling exponent Delta =1, a value that differs from previous estimates.

Monte Carlo evaluation of hadron masses in lattice gauge theories with fermions

An improved Monte Carlo method is presented for lattice gauge theories withfermions. Taking the pion mass and meson Regge trajectory slope as input, this procedure is used to calculate the rho mass on lattices up to 12 4 for gauge group¯I, the best discrete approximation to SU(2). The final result is m ρ=670±100MeV. Arguments are given to show that this prediction would be changed by replacing¯I by SU(2) or SU(3).

Evaluation of radiation fields using statistical methods of integration

An improved Monte Carlo method of integration is used to evaluate the radiation fields of a large linear antenna and a large aperture antenna. When compared with the conventional numerical methods of integration, the improved Monte Carlo method saves a considerable amount of effort and time, yet it still gives reasonably accurate results.