000000 o 0oooooooo 0oo
100 200 300 400 500 600 700 800 900 1000
100 200 300 400 500 600 700 800 900 1000
Figure 4-10. Monte Carlo vs. Exact results for M = 3. The upper figure shows three
curves, the upper one corresponding to ({P) and the lower ones to (PI) and
(P3') which by symmetry should be exactly the same as <,., v are in the exact
solution. The circles are results from the Monte Carlo simulation but the
solid lines are from the numerical diagonalization of 73. The lower figure
also has three curves corresponding to ({P) and (P2) and (P3) but shows
the difference A, between the exact results and the simulation. Clearly the
errors are quite correlated in j as for the M = 2 case. The data is obtained
with g = 0.4, p = 1 and To = 4. The simulation had a total of 700,000 sweeps
using the last 90% for data gathering. The fixed spin was at (i,j) = (1,500).
with KP an NA-by-Nc hermitian matrix field in two-dimensions as in Eq. (2-1), the authors
work out the Lightcone time evolution operator:
P- (x+) dx-Tr PDK2 (
J 2
ADK 3\
3 JN
(4-40)