Bornholdt's heterogeneous agent-based spin model for financial markets
Previously we have discussed ant colony model [1, 2] (see Kirman's agent based and stochastic model of ant colony), which is an interesting example of applying knowledge obtained from one field to another. Human (ex., trader in the financial markets) crowd behavior is ideologically quite similar to the behavior in ant colonies, thus the success and relevancy of the aforementioned model were to be expected. Though the key to success lies in the description of large number of entities.
Interestingly enough one can also create, and thus provide additional backing for the argument above, a successful model for human crowd behavior using classical models of statistical physics as an inspiration. In this text we will discuss agent-based spin model of the financial markets proposed by Bornholdt [3, 4], which is based on widely known Ising model. Despite the fact that Ising model models inanimate system, natural interactions are introduced by assuming two different types of interactions between the agents - local herding (local feromagnetic interaction) and global minority game (coupling with total magnetic field generated by whole lattice).
Bornholdt's model is also interesting as recently there were some attempts to propose macro treatment of the original agent-based model [5]. Previously similar thing was done with Kirman's model [2].