Around the ising model

Abstract

This chapter 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.