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Bali's Ancient Rice Terraces: A Hamiltonian Approach.

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We developed a Hamiltonian model for Bali's Subak irrigation system, revealing a power-law distribution in rice field clusters. The model identifies two equilibria and critical phase transitions, extending physics to human-environmental systems.

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Area of Science:

  • Complex Systems Science
  • Environmental Physics
  • Sociophysics

Background:

  • The Subak system is a centuries-old Balinese agricultural practice.
  • Understanding the dynamics of coupled human-environmental systems is crucial.

Purpose of the Study:

  • To model the Balinese Subak irrigation system using a Hamiltonian approach.
  • To analyze the cluster-size distribution and equilibrium states of the system.

Main Methods:

  • Development of a Hamiltonian model incorporating local and long-range interactions.
  • Analysis of cluster-size distribution, identifying a power-law with exponent ~2.
  • Finite-size scaling analysis to study phase transitions and critical phenomena.

Main Results:

  • The model reproduces the power-law cluster-size distribution of rice-field patches.
  • Two distinct equilibrium states were identified, driven by energy-entropy balance and specific interactions.
  • Critical transitions were observed, with a global antiferromagnetic interaction influencing the system's behavior.

Conclusions:

  • The Hamiltonian framework can effectively model complex human-environmental interactions.
  • The study provides insights into the emergent properties of the Subak system.
  • This approach offers a new perspective on analyzing socio-ecological systems.