How to include disorder in the numerical computation?

[PRB147]

For example, in tight binding model, the site energy is random
I want to have 100 disorder realizations, then I have the following
two questions:

1. Do different realization needs different seed in the random number generation subroutine?

2. When all realizations are completed, the result should be the simple average? (i.e., $$\frac{\sum_{n=1}^{100} P_n}{100}$$.
)
Please help me, if you know, Thank you in advance!

 

[ZapperZ]

Whenever one needs to include some "random" processes in a particular calculation or modeling, one tends to use some form of Monte Carlo algorithm. Not sure if this is applicable to you, but it is used a lot in different areas of physics.

Zz.

 

[PRB147]

Thanks you, Zz, you are right.