Monte Carlo Pure-model Calculations

Roland Assaraf, Michel Caffarel, Anatole Khélif

In this paper we discuss various aspects of diffusion Monte Carlo methods using a fixed number of walkers. First, a rigorous proof of the divergence of pure diffusion Monte Carlo (PDMC) methods (DMC without branching in which the weights are carried along trajectories) is given. Second, a bias-free Monte Carlo method combining DMC and PDMC approaches, and based on a minimal stochastic reconfiguration of the population, is discussed. Finally, some illustrative calculations for a system of coupled quantum rotators are presented.

H. Jirari, H. Kröger, X.Q. Luo +1 more

J. Eckert, M. Fähnle

Taking into account quadratic corrections to the linearized renormalization transformation, a simple expression for the transient behavior of the local eigenvalues obtained from a Monte Carlo renormalization-group (MCRG) analysis is derived, which constitutes a basis for extrapolation procedures commonly used in MCRG calculations. The method is applied to investigate the effect of irrelevant and relevant scaling fields for the d=2 Ising model. It is shown that the transient effect for the magnetic eigenvalue is very fast because it is dominated not by the largest, but by the second largest irrelevant scaling exponent. Peculiarities observed for the effect of the relevant thermal scaling field \ensuremath{\tau}=${\mathit{a}}_{\ifmmode\pm\else\textpm\fi{}}$(T-${\mathit{T}}_{\mathit{c}}$)/${\mathit{T}}_{\mathit{c}}$ may be interpreted by assuming ${\mathit{a}}_{+}$\ensuremath{\ne}${\mathit{a}}_{\mathrm{\ensuremath{-}}}$, i.e., a nonanalytic scaling field.

Hamza Jirari, H. Kröger, Chunqing Huang +3 more

James C. Greer

Ole G. Mouritsen, Svend J. Knak Jensen, B. Frank

Ising models on fcc lattices with pure three-spin or pure four-spin interactions are shown by Monte Carlo calculations to exhibit only one phase transition which is of first order. The transition temperature of the model with pure four-spin interactions differs from the Onsager result. This implies that the model is likely not to possess a self-dual property as claimed by Wood.