On the mean Euler characteristic and mean Betti numbers of the Ising model with arbitrary spin

Details On the mean Euler characteristic and mean Betti numbers of the Ising model with arbitrary spin On the mean Euler characteristic and mean Betti numbers of the Ising model with arbitrary spin

2006-01-16

arxiv.org/abs/cond-mat/0601344v2

Physics

Condensed Matter

Statistical Mechanics

12 pages

Scientific paper

10.1088/1742-5468/2006/03/P03011

The behaviour of the mean Euler-Poincar\'{e} characteristic and mean Betti's numbers in the Ising model with arbitrary spin on $\mathbbm{Z}^2$ as functions of the temperature is investigated through intensive Monte Carlo simulations. We also consider these quantities for each color $a$ in the state space $S\_Q = \{- Q, - Q + 2, ..., Q \}$ of the model. We find that these topological invariants show a sharp transition at the critical point.

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