is the values of all fields and spins on the lattice, is used to calculate a '1. 11 property
of the : in that state (the correlation between : values at different lattice sites is
a t 1 ...1 ..:.. y to investigate). \We refer to this as taking a .:.. )le of the i. :.. or
simply, dling the system. After sampling we proceed to complete another sweep, the
ob'i 'vc being to collect a large number of samples which we use to obtain statistically
relevant information about the nnm.
Even though changes in the physical action determine the evolution of the i :.. as
we progressively perform more and more sweeps, it is possible that we start out from a.
very unphysical state. T-: means that it may take many sweeps, i.e., a long Monte Carlo
time, for the to be in a physically favored state. We do not want the arbitrary
(and quite possibly "high] ..;") initial state of the .-.m to affect the statistical
integrity of the sample distribution we use to calculate p1. 1 "-'operties of the i.
To prevent this, it is common practice to ': the : before samples are taken.
TI. is done '1 performing until the state of the is in a region of state
space which is favored '. the pl '. action.
Having described in broad terms the basic ideas it is in order to -.1 .' 1 in more
detail, the before mentioned Metropolis algorithm: It is in primn' a very -... method
(although details quickly become somewhat involved) and we can summarize it as follows:
1. Initialization. Construct the I'm model ob' 1 S which manages and stores the
complete state of the '. i.e., values of all fields and spins.
2. I 0 ... :on. Perform sweeps on S until relaxation criteria is met. In each sweep:
1. At a given site :: a change in field configuration, and calculate the tance
probability.
2. A(.. or decline the change by .. a. random number to the 1. ,' lity.
3. Go to another site and repeat these steps until sweep is done.
but in the current work we visit sites in a. deterministic order, allowing each site to be
visited exactly once in a sweep