Agent-based generalized spin model for financial markets on two-dimensional lattices

We study a microscopic model for price formation in financial markets on a two-dimensional lattice, motivated by the dynamics of agents. The model consists of interacting agents (spins) with local and global couplings. The local interaction denotes the tendency of agents to make the same decision as their interacting partners. On the other hand, the global coupling to the self-generating field represents the process which maximizes the profit of each agent. In order to incorporate more realistic situations, we also introduce an external field which changes in time. This random field represents any internal or external interference in the dynamics of the market. For the proper choice of model parameters, the competition between the interactions causes an intermittency dynamics and we find that the distribution of logarithmic return of price follows a power law.