The Fast Linear Algorithm
for O(1) symmetry (-1<S<1)
Probabilities and Performances :

The Fast Linear Algorithm is the fastest of all algorithms proposed. Indeed we can show generally that another algorithm cannot be faster (see article).
  • Figure: The probability P(x) and the test function f(x) for various algorithms.
    • FLA=Fast Linear Algorithm
    • AW=Alias Walker
    • AWH=Alias Walker Hasting
    • DHB=Direct Heat-Bath
    • Me  =Metropolis
    • P5 =P(x) with h=5
    • P10=P(x) with h=10
 
  • Figure: comparison of the time of simulation for various algorithms for the two and three dimensional antiferromagnetic triangular lattices (2t and 3t) and the ferromagnetic square lattices (2c)
    The critical temperatures are shown by the squares
    • FLA=Fast Linear Algorithm
    • AW=Alias Walker
    • AWH=Alias Walker Hasting
    • DHB=Direct Heat-Bath
    • Me  =Metropolis
 
 
  • Figure: comparison of the rate of simulation for various algorithms for the two and three dimensional antiferromagnetic triangular lattices (2t and 3t) and the ferromagnetic square lattices (2c)
    The critical temperatures are shown by the squares
    • FLA=Fast Linear Algorithm
    • DHB=Direct Heat-Bath
    • AW=Alias Walker
    • AWH=Alias Walker Hasting
    • Me  =Metropolis