For the Ising model, the obvious change in the configuration is to try to
update (or ``flip'') a spin, i.e. flip the sign (or direction) of the spin
variable. If we try to change many spins at once, 
will be
large, so the probability to accept the change, 
, will be
small. So update a single spin at a time.
For a single spin flip, 
depends only on the spin values at the
site and its nearest neighbors, i.e. the update is local.
If 
, we make the proposed change.
If 
, we make the change with probability 
.