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Article Dans Une Revue Journal of Statistical Mechanics: Theory and Experiment Année : 2006

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

Résumé

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 $S_Q = \{ - Q, - Q + 2, \ldots, Q \}$ of the model. We find that these topological invariants show a sharp transition at the critical point.
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Dates et versions

hal-00016966 , version 1 (14-01-2006)
hal-00016966 , version 2 (13-02-2006)

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Philippe Blanchard, Christophe Dobrovolny, Daniel Gandolfo, Jean Ruiz. On the mean Euler characteristic and mean Betti numbers of the Ising model with arbitrary spin. Journal of Statistical Mechanics: Theory and Experiment, 2006. ⟨hal-00016966v2⟩
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