Around the Ising Model

Sergio Rica

This article discuss several features and connections arising in a class
of Ising-based models, namely the Glauber-Ising time dependent model, the Q2R
cellular automata, the Schelling model for social segregation, the decision-choice
model for social sciences and economics and finally the bootstrap percolation model
for diseases dissemination. Although all these models share common elements, like
discrete networks and boolean variables, and more important the existence of an
Ising-like transition; there is also an important difference given by their particular
evolution rules. As a result, the above implies the fact that macroscopic variables
like energy and magnetization will show a dependence on the particular model chosen.
To summarize, we will discuss and compare the time dynamics for these variables,
exploring whether they are conserved, strictly decreasing (or increasing) or
fluctuating around a macroscopic equilibrium regime.