Can φ⁴ lattice fields model financial markets?
Lattice field theory as a multi-agent system of financial markets
This paper explores using a modified φ⁴ lattice field theory as a multi-agent system to simulate financial markets. Each lattice site represents an agent deciding to buy or sell, influenced by neighbors (herding) and a global field pushing towards the majority or minority opinion. This creates a system with competing dynamics, leading to phenomena like market bubbles and crashes.
Key points for LLM-based multi-agent systems: The continuous values of the φ⁴ model, versus the binary values in Ising models, offer greater expressiveness for agent states (e.g., strength of conviction). The competing dynamics driven by local and global influences, implemented via Gibbs sampling and a modified acceptance/rejection step, provides a mechanism for complex agent interaction. This approach could be adapted for other multi-agent scenarios where continuous variables and competing influences are relevant.