Modeling of price and profit in coupled-ring networks

We study the behaviors of magnetization, price, and profit profiles in ring networks inthe presence of the external magnetic field. The Ising model is used to determine thestate of each node, which is mapped to the buy-or-sell state in a financial market, where+1 is identified as the buying state, and −1 as the selling state. Price and profit mechanisms are modeled basedon the assumption that price should increase if demand is larger than supply, and itshould decrease otherwise. We find that the magnetization can be induced between two ringsvia coupling links, where the induced magnetization strength depends on the number of thecoupling links. Consequently, the price behaves linearly with time, where its rate ofchange depends on the magnetization. The profit grows like a quadratic polynomial withcoefficients dependent on the magnetization. If two rings have opposite direction of netspins, the price flows in the direction of the majority spins, and the network with theminority spins gets a loss in profit.