Bali's Ancient Rice Terraces: A Hamiltonian Approach

We propose a Hamiltonian approach to reproduce the relevant elements of the centuries-old Subak irrigation system in Bali, showing a cluster-size distribution of rice-field patches that is a power-law with an exponent of ∼2. Besides this exponent, the resulting system presents two equilibria. The first originates from a balance between energy and entropy contributions. The second arises from the specific energy contribution through a local Potts-type interaction in combination with a long-range antiferromagnetic interaction without attenuation. Finite-size scaling analysis shows that, as a result of the second equilibrium, the critical transition balancing energy and entropy contributions at the Potts (local ferromagnetic) regime is absorbed by the transition driven by the global-antiferromagnetic interactions, as the system size increases. The phase transition balancing energy and entropy contributions at the global-antiferromagnetic regime also shows signs of criticality. Our study extends the Hamiltonian framework to a new domain of coupled human-environmental interactions.