Is there any way to check whether in a Monte Carlo simulation using Ising model is stuck in any (false) local minima of energy or not, particularly in 3D system ?
For nearest-neighbor interactions in 1D and 2D, the free energy of the system can be computed analytically. We can then check that this free energy is at its global minimum for a certain state. In 3D, we do not know the free energy analytically, so we have to resort to some kind of simulation (Monte-Carlo probably). If you reach a final state of your simulation, you can always give it a 'kick' and check that it comes back to the same state. This can't rule out the possibility of very deep local minima, but it does increase your confidence that you have found the ground state.
For situations where the Ising model DOES get trapped in a local minimum, check out the work of Sidney Redner at Boston University. The gist is that if you quench the system, it can get 'stuck' in local minima and the dynamics are surprisingly non-trivial (in 2D and 3D, the 1D system always goes to the ground state).