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Phase Transitions in a 2D Ising Model of Agent Expectations in Financial Markets: Analytics in One- and Two-Dimensional Network Topologies
  • Marko Raseta,
  • Steven Silver
Marko Raseta
Erasmus Universiteit Rotterdam
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Steven Silver
San Jose State University
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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.

Peer review status:UNDER REVIEW

24 May 2021Submitted to Mathematical Methods in the Applied Sciences
02 Jun 2021Assigned to Editor
02 Jun 2021Submission Checks Completed
01 Sep 2021Reviewer(s) Assigned