Table 4-5. Monte Carlo vs. Exact results for M 2. Table showing fitted GC from a
Monte Carlo run with M 2 vs. exact values that can be calculated in this
special case.
fitted Gs exact GC remark
0.2404 0.21333 Sweeps: 7 10, x = 0.6 and To = 4
0.1602 0.13291 Sweeps: 7 105,x = 0.6 and To = 6
0.3672 0.39814 Sweeps: 7 10s, x 0.8 and To 3
0.1602 0.16821 Sweeps: 1.5- 106, x =0.6 and To 6
makes this method for solving the problem intractable as M starts to really grow. In
contrast, the Monte-Carlo simulations only get linearly more computationally intensive as
M grows. We shall discuss this fact more in the next section.
4.3 A Real Test of 2D Tr03
The previous tests have shown that the Monte Carlo simulation captures at least
some of the features of the model it is set out to simulate. However, the comparison so
far has only been between two views of the Lightcone World Sheet picture. As a last test
we search the literature for known results for 2D Tr03 matrix quantum field theory to
compare. Such a test not only confirms that the computer simulation works, but that the
Lightcone World Sheet picture describes the field theory that is should.
In 1992 Dalley and Klebanov [22] studied a two-dimensional, Lightcone quantized,
large N, matrix field theory. They showed that in the theory possessed closed string
excitations which became free in the Nc -- +oc limit. As is done in the Lightcone World
Sheet picture, 'l .r discretize the longitudinal momentum and obtain a linear Schr6dinger
type of equation for the string spectrum which ],. v tackle numerically by diagonalizing
the matrix representing the Hamiltonian. The discretization makes the matrix formulation
possible and the matrix is of finite size in the presence of the cutoff which is imposed by
considering a string state with a given longitudinal momentum. Their work has an entirely
different agenda than the work presented here; 'l,. v are interested in string theoretical
implications of the string spectrum. As is done in the Lightcone World Sheet picture the
cutoff is removed by taking the momentum resolution to infinity, holding the momentum