The Fast Linear Algorithm
for O(3) Phi^4 spin model
Probabilities and Performances :

The Alias Walker Hasting algorithm is the fastest of all algorithms proposed.
  • Figure: The probability P(x) and the test function f(x) for various algorithms.
    • AWH = Alias Walker Hasting algorithm
 
  • Figure: comparison of the time of simulation for various algorithms for the three dimensional cubic ferromagnetic lattices. The drop of efficiently at low temperature (high h) is due to the too small number of points. We should use the trick (dividing the interval [xini,xfin] between [xini,xH] and [xH,xfin]) introduced for infinite Ising spins O1_Alias_Walker.html.
    The critical temperature is shown by the squares
    • AWH = Alias Walker Hasting algorithm
    • FLA2=Fast Linear Algorithm for x then for y.
    • Med = Metropolis restricted to an interval d
    • Me2d = Metropolis restricted to an interval d first for x then for y.
  • Figure: comparison of the rate of simulation for various algorithms for the three dimensional cubic ferromagnetic lattices.
    The critical temperature is shown by the squares
    • AWH = Alias Walker Hasting algorithm
    • FLA2=Fast Linear Algorithm for x then for y.
    • Med = Metropolis restricted to an interval d
    • Me2d = Metropolis restricted to an interval d first for x then for y.