Number of Magic Squares from Parallel Tempering Monte Carlo

@article{Pinn1998NumberOM,
  title={Number of Magic Squares from Parallel Tempering Monte Carlo},
  author={K. Pinn and C. Wieczerkowski},
  journal={International Journal of Modern Physics C},
  year={1998},
  volume={09},
  pages={541-546}
}
There are 880 magic squares of size 4 by 4, and 275 305 224 of size 5 by 5. It seems very difficult if not impossible to count exactly the number of higher order magic squares. We propose a method to estimate these numbers by Monte Carlo simulating magic squares at finite temperature. One is led to perform low temperature simulations of a system with many ground states that are separated by energy barriers. The Parallel Tempering Monte Carlo method turns out to be of great help here. Our… Expand

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