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

Abstract

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 $S\_Q=\{-Q,-Q+2,...,Q\}$ of the model. We find that these topological invariants show a sharp transition at the critical point.

12 pages

References in corpus (1)

• Critical Binder cumulant in two-dimensional anisotropic Ising models