On the mean Euler characteristic and mean Betti numbers of the Griffiths' model.
Résumé
The behaviour of the mean Euler-Poincaré characteristic and mean Betti's numbers in the Griffiths' model on Z^2 (the Q-states Ising model) 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.