Bali's ancient rice terraces: A Hamiltonian approach

TL;DR

This paper introduces a Hamiltonian model to simulate Bali's ancient Subak irrigation system, revealing complex phase transitions and cluster distributions, thus extending physical models to human-environment interactions.

Contribution

It presents a novel Hamiltonian framework capturing the dynamics of Bali's rice terraces, incorporating both local and long-range interactions, and analyzes phase transitions in this socio-environmental system.

Findings

Cluster-size power-law distribution observed.

System exhibits two equilibria involving energy and entropy.

Weak-first order phase transition identified at the thermodynamic limit.

Abstract

We propose a Hamiltonian approach to reproduce the relevant elements of the centuries-old Subak irrigation system in Bali, showing a cluster-size power-law distribution. The resulting system presents two equilibria. The first balance is between energy and entropy contributions. The second lies in the energy contribution: a local Potts-type interaction and a long-range anti-ferromagnetic one without attenuation. Finite-size scaling analysis shows that as a result of the second balance, the transition balancing energy and entropy contributions for low values of the antiferromagnetic contribution is absorbed by the transition for high values of that contribution as the system size increases. The system thus presents only a weak-first order phase transition at the thermodynamic limit. This extends the Hamiltonian framework to a new domain of coupled human-environmental interactions.