Tax evasion study in a society realized as a diluted Ising model with competing interactions

Abstract: In this research, the tax evasion percentage, as order parameter, of a system of individuals or agents inscribed in a $N = L \times L$ 2D square grid is computed. The influence of local environment over each agent is quantified both through competitive exchange integrals (ferromagnetic and antiferromagnetic bonds) and dangling bonds randomly distributed, which allows to identify the system with disordered ternary alloys of the type $\mathrm{A_\textit{p}B_\textit{x}C_\textit{q}}$ with a certain stoichiometry $(p,x,q)$ particular of each society. Our proposal is based on the so-called spin glass phase present in magnetic systems characterized by disorder, dilution and competitive interactions where magnetic frustration can take place, resembling the way as an individual or agent in a society is able to face a decision. In this sense, agents are identified as Ising spins, which can take two possible values ($\sigma = \pm 1$), in correspondence with a two-state system where agents can be tax compliant or not. Such an identification between social and physical variables, as well as parameters like an external applied magnetic field or temperature, are topic of discussion in this investigation. Thermalization of the observables is carried out by means of the heat bath algorithm. Other social variables, such as the audit period, and its effects over the percentage of evasion, are used to analyze the behavior of tax evasion in Colombia, however the model can be applied to any country.