separated set of files and can be replaced without consequences to the rest of the computer
program.
Consider the following action:
M-1
S = a (qk+l qk)2 with qo q= M = 0. (4-7)
k-0
As before, use the following:
q= (qi, q2, ... qM-1), Dq= dx dx2... dxM-1, Z = qe- S(q). (48)
With the very simple observable operator q -> Ok (q) = qk q1 the expectation value
becomes
(Okl) = qe-S(q)Okl qkql}) = min(k, 1) (M- max(k, 1)) (4-9)
We use this result to find the expectation value F(k, 1) = ((qk q,)2
F(k, 1) ((qk 2) (q 2(qk qi) + (q
SMIk II(M- Ik 1) (4-10)
2aM
so we can consider the function of the difference only f(m) = F(k, k + m). Without any
loss of generality we take k = 0 and the behavior of f as m ranges from 1 to M 1. The
results for a MC-simulation are shown in Figure 4-1 together with the above exact answer.
The relative agreement allows us to consider this test passed by the simulation software.
To see the computer implementation of the bosonic chain presented here see Appendix A.
4.1.4 Another Simple Example: ID Ising Spins
The spin system si, which plays a vital role in the Lightcone World Sheet formalism,
has often been likened to an Ising spin system. This is of course true because the spins, as
in Ising's model for ferromagnetism take on the two values s' =T and s' =- implemented
on a computer with s\ = +1 and s =- -1. A ID Ising spin system is therefore exactly as