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

The behaviour of the mean Euler–Poincaré characteristic and mean Betti's numbers in the Ising model with arbitrary spin on as functions of the temperature is investigated through intensive Monte Carlo simulations. We also consider these quantities for each colour 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.