configurations on the two dimensional lattice representing the discretized world sheet.
'. will -- 'y the :. etropolis Algorithm to construct the i : ')v sequence and it works
as follows: Given a field configuration q, we
1. Visit a site in q, and alter the field values there and possibly in the immediate
vicinity to obtain a new configuration q'.
2. Calculate x = exp{-(S(q ) S(qi)} and have a computer calculate a random number
y between 0 and 1.
3. If y < x accept the change and go back to the first. with q[ as qg, otherwise return
to the first I ix without modification.
As before, we cannot take the Markov sequence to be (. ): q[ is too correlated with
qi. In the terminology of the last section we can --:- that updating only a single site
constitutes too small a difference Ax between successive Markov ... elements.
Swe continue and repeat the three steps above. ".'.h.en they have been repeated
the same number of times as there are lattice sites we consider a sweep of the lattice to
be complete. Sites can be visited either at random or sequentially. When enough sweeps
have been done on a lattice configuration for it, to be ::ci( 1 uncorrelated with the
original one we accept it as and proceed again from this configuration to obtain m
another one: .. By sufficiently we mean that .' and qi+2 are completely uncorrelated
and we find the number of s--- -- required for this with extensive testing. In '.'e this
choice of sample rate is not rigorous but as mentioned in the last section, we still average
over the intermediate states. '- -efore, this ": out" of states will not affect the
mean value of the operator but only the uncertainty anal of it.
4.1.3 A Simple Example: Bosonic Chain
In order to test the application of the Monte Carlo method in this setting, and the
computer code in .. ticular, we start with an extremely :. .'. example. Because of the
the :::>uter code is organized, this test applies to a large extent the same code as
will later be used in more complex ins. S :.. -: fic functions reside in a neatly