On the mean Euler characteristic and mean Betti numbers of the Ising model with arbitrary spin
Philippe Blanchard, Christophe Dobrovolny, Daniel Gandolfo, Jean Ruiz
Abstract
The behaviour of the mean Euler-Poincaré characteristic and mean Betti's numbers in the Ising model with arbitrary spin on Z2 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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