Phase Transitions in a 2D Ising Model of Agent Expectations in Financial
Markets: Analytics in One- and Two-Dimensional Network Topologies
Abstract
Phase transitions between ordered and disordered states of interactive
agents have been recognized as integral to dynamics in a range of
economic and social processes. Several theorists in the study of
financial markets have directly linked phase transitions between
disordered and ordered states of agents to a critical point in the
dynamics of market price. To date, phase transitions in the dynamics of
price in financial markets have been demonstrated with numerical
methods. In an application to a financial market, we propose a
multicomponent in which a first component is in bounded rationality and
a second component is in behavior that generates herding in financial
markets. A transition function defines the relative weight of
components. We extend conditions of Onsager (1944) for phase transitions
in a 2D Ising model and analytically demonstrate that the proposed model
evidences phase transitions. Generalizations of the results to other
multi-component models are noted.