- Figure: comparison of the time consumption to simulate
a two dimensional ferromagnetic square lattice for various algorithms
(Metropolis,Me, Restricted metropolis, Med, Direct Heat Bath, DHB,
Walter Algorithm for 4 spins on a plaquette, WA4,
Restricted Walter Algorithm Hasting for 4 spins on a plaquette, WAH4d)
The critical temperatures are shown by the squares
The restricted Metropolis Algorithm is the fastest at the critical temperature.
We can show more generally that this conclusion holds whatever the system is.
It is mainly due to the presence of zero local field (see article). The Ising ±1
case is the only one where the Metropolis is better than the Heat Bath.