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

Philippe Blanchard·Christophe Dobrovolny·Daniel Gandolfo·Jean Ruiz
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Abstract

The behaviour of the mean Euler-Poincaré 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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Philippe Blanchard, Christophe Dobrovolny, Daniel Gandolfo, Jean Ruiz. 2006-02-13. On the mean Euler characteristic and mean Betti numbers of the Ising model with arbitrary spin. https://doi.org/10.1088/1742-5468%2F2006%2F03%2Fp03011

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