Pictorial View of
Example 3: Lattice
Choice of Points in Lattice Monte Carlo
Assume you have a particular choice
is a tiny number (as
is energy of full system
is approximately the number of objects in system) and more importantly, varies rapidly.
Thus, we cannot choose points ``uniformly''.
Rather, we assume point
. So that
only changes a little. This can be achieved by only changing one of the spins at a time, i.e., we move
Typically, this produces a change
is energy per site (up to numerical constants).
Remember classical result of energy of
per degree of freedom.
So change in
Thus, we will not move off ``peak'' of integrand.
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