Philippe Blanchard, Christophe Dobrovolny, Daniel Gandolfo, Jean Ruiz
Published 2006-01-16, updated 2006-02-13Version 2
The behaviour of the mean Euler-Poincar\'{e} 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.
Decay of the metastable phase in d=1 and d=2 Ising models
Finite-size scaling and conformal anomaly of the Ising model in curved space
Phase diagram and exotic spin-spin correlations of anisotropic Ising model on the Sierpiński gasket
