Conferences & Workshops

Critical Phenomena in Financial Markets and Social Networks

by Christoph Schmidhuber

Main/0-174 - Auditorium (Main)

Main/0-174 - Auditorium


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Analogies between financial markets and critical phenomena have long been observed empirically. In particular, the variance of financial market returns can be measured to scale as a certain power of the time horizon, the so-called second Hurst exponent. More recently, an analog of the Landau potential has indirectly been measured. So far, no convincing theory that can explain these empirical observations has emerged as a consensus.

In this informal talk, we propose a step towards such a theory by modeling financial markets as a lattice gas. The lattice represents the social network of investors, and the gas molecules represent the shares of an asset that are distributed across this network. In efficient markets, it is argued that arbitrageurs drive this lattice gas to its critical temperature, where it undergoes a second-order phase transition in analogy with water and steam. There, it is described by a renormalizable field theory and characterized by universal critical exponents. We show that this can not only replicate the empirically observed second Hurst exponent, but it also allows us to infer the fractal dimension D of the presumed underlying social network. 


In the case of a trivial network topology, consistency with empirical observations would imply a dimension D near 3. However, to model realistic networks, the approach must be extended in the future to more complex network topologies and to more subtle variants of the lattice gas. This will also require a generalization of field theory from manifolds to networks. It may lead to a new and deeper understanding not only of financial markets, but of social networks in general. 

Relevant Publications:

Financial Markets and the Phase Transition between Water and Steam (C. Schmidhuber, Physica A, 2022)

Trends, Reversion, and Critical Phenomena in Financial Markets (C. Schmidhuber, Physica A, 2021)