Monte-Carlo simulation for a matrix model

[mvachovski]

Hello there,

I am writing a Monte-Carlo simulation for a matrix model with a Lagrangian consisting
of two parts - Yang-Mills and Chern-Simons type terms. As I am accepting/rejecting
new states with probability P=min{1, dL}, where dL is the change of the lagrangian.

But then there is something weird. When I plot the values of the YM and CS terms as functions
of the Monte-Carlo time, it seems that the system "starts" in a state that both terms are small,
but after some time the terms become significantly bigger and there is "the equilibrium"
And this effect is because the YM and CS terms have such sings that big values of them cancel
and still can produce a small value for the Lagrangian, but this would simply mean that the equilibrium
of the system is a state with a bigger energy! Is this behavior proper/expected or I am doing
something wrong?

Thanks in advance

P.S. I'm uploading the plot of the YM and CS over Monte-Carlo time.

 

[mvachovski]

Hi all,

For those which could encounter the same situation.
As I learned a bit more about the model it seems, that really should be the equilibrium
state of the system. So for generic system which is simulated by Monte-Carlo methods
this could happen.

Cheers