Alias Walker Hasting* Algorithm
for O(2) symmetry



Spins with one components: S=x
local field : hlocal=(hlocalx)
Energy=-S.hlocal=-hlocal.x
P(x)=e-Energy/T.dx
       =eh.x.dx
The Alias Walker Hasting (AWH) Algorithms use the rejection method with a function consisting of n steps (see the figure and article for more details). In this page (AWH_*) the probability to produce the alias is made of a histogram at one temperature. It is therefore an average of all values of the local field at this temperature.

Download the Alias Walker Hasting (AWH) Algorithms:
1.  To use the Alias Walker (AW) and Alias Walker Hasting (AWH) Algorithms you must have :
2.  AND you must have the tables in the file "XX_walker_histo.res". Two choices: . You can choose to download the file O2_walker.res already done or make one with create_O2_walker.c
  • XX_walker_histo.res   valid around T=Tc=0.512 for the two dimensional antiferromagnetic triangular lattices. Done with 100 bins
 or To use create_XX_walker_histo.c you must have the histogram (XX_walker_histo_histogram.res) created before by Monte Carlo (for example by Metropolis) at the choosen temperature. It is given for T=Tc=0.512 for the two dimensional antiferromagnetic triangular lattices. To get a similar C Program for TWO variables: ../O3_Phi4/index.html

Download the Article:

Probabilities and Performances :
  • Figure: comparison of the time of simulation for various algorithms for the two dimensional antiferromagnetic triangular lattices.
    The critical temperatures are shown by the squares
    The Fast Linear Algorithm (FLA) is the fastest of all algorithms proposed and 25 to 100% faster than the Alias Walker Hasting* algorithm.
    More...

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