  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.
