A Network-Based Stochastic Model of Conflict and Cooperation 

We present a physics-based framework for modeling geopolitical relationships using a spin-glass approach. We use the Russo-Ukrainian conflict as a case study. In this model, the conflict is treated as a system of interacting “spins” representing key entities: Ukraine, Russia, the European Union, and the United States. The interactions between nations are quantified by Ising-type coupling constants, which encode cooperative or antagonistic tendencies, and by localized external fields, representing each nation’s internal pressures and policy drivers. The model evaluates the system’s total Hamiltonian energy to determine the stability of the geopolitical configuration, with low-energy states corresponding to stable equilibria. Concepts such as frustration and hysteresis are reinterpreted in political terms to describe partial ceasefires, historical path dependencies, and shifting alliances. Although simplified, the model demonstrates how statistical physics methods can be adapted to social systems to capture determinants of stability. We drew inspiration from purely sociological network models such as the Additive and Multiplicative Effects Model and the Exponential Random Graph Model. Future work will expand the framework to include concepts from sociological models and refined data inputs with the goal of deriving emergent effects and developing predictive simulations of policy shifts and conflict stability.