 Figure: The probability P(x) and the test function f(x) for various algorithms.
 FLA=Fast Linear Algorithm
 AWH=Alias Walker Hasting
 Me =Metropolis
 d =Metropolis with restriction
 Mo=Moriarty
 G =Gaussian
 H =Hattori
 P_{4}=P(x) with h=4




 Figure: comparison of the time of simulation for various algorithms
and various systems.
The critical temperatures are shown by the squares
Metropolis/FLA for the:
 2c=two dimensional square lattices with ferromagnetic interactions
 2t=two dimensional triangular lattices with antiferromagnetic interactions
 3t=three dimensional triangular lattices with antiferromagnetic interactions
 4s=four dimensional cubic lattices with ± interactions (the exchange MC algorithm is also used)


for the 2 dimensional triangular antiferromagnetic system with XY spins.
 FLA=Fast Linear Algorithm
 AWH=Alias Walker Hasting
 Me =Metropolis
 d =Metropolis with restriction
 Mo=Moriarty
 G =Gaussian
 H =Hattori


 Figure: comparison of the rate of simulation for various algorithms
for the 2 dimensional triangular antiferromagnetic system with XY spins.
 FLA=Fast Linear Algorithm
 AWH=Alias Walker Hasting
 Me =Metropolis
 d =Metropolis with restriction
 Mo=Moriarty
 G =Gaussian
 H =Hattori
The critical temperature is shown by the squares

