Why the monte carlo integrator is having different probability of acceptance and rejection ?

[AMRENDRA KUMAR]

Simulation run time [s]: 26439.8
Monte Carlo statistics:
Total moves: 164167680000
84.7054% Accepted
15.2946% Rejected

I have included the material file and input file.
I have also included the snippet of ucf file.
Any suggestions are welcomed 

Best Regards,
Amrendra Kumar

[AMRENDRA KUMAR]

[Luke Elliott]

Hi Amrendra,

There are two parts to this question; what is the Monte-Carlo integrator, and why are you seeing a much higher percentage of accepted moves?

In brief terms, the Monte-Carlo integrator works as follows:

Monte-Carlo integrator

1. Randomly choose a spin and randomly modify its spin direction - a trial move

3. Calculate new system energy using new spin direction

4. If system energy is lower, accept the move, otherwise the move is accepted/rejected based on a test against a temperature dependent probability distribution.

This makes the Monte-Carlo integrator useful for finding ground-state configurations/statistics as it rapidly minimises the energy in the system.

For full details see Section 4.4 of the primary VAMPIRE paper.

Accepted/rejected moves percentage

In the case of your simulations, you are seeing a very high percentage of accepted moves. This would suggest that your system is either not reaching equilibrium, or is only just reaching equilibrium before the end of the simulation.

Looking at your input files, you are using a very low number of time-steps for your simulation which may not give enough time for the system to reach equilibrium. I'm not particularly familiar with YIG but I see you initialise the system in the [0,0,1] direction for [20,20,5] dimensions, i.e. out of plane, with no uniaxial anisotropy. I would naively expect the system to relax to an in-plane magnetisation which would also possibly explain why your system has a high number of accepted moves.

The simplest solution would be to increase the number of time steps significantly until your percentage accepted moves reaches a lower percentage, checking against the output statistics and spin configurations to see if these appear reasonable. I'd suggest 100,000 steps aiming for an acceptance rate of ~5%.

Best,

Luke