Bali’s Ancient Rice Terraces: A Hamiltonian Approach,Physical Review Letters

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Bali’s Ancient Rice Terraces: A Hamiltonian Approach
Physical Review Letters ( IF 8.1 ) Pub Date : 2021-10-14 , DOI: 10.1103/physrevlett.127.168301
Yérali Gandica ₁ , J Stephen Lansing _{2,

3} , Ning Ning Chung ₄ , Stefan Thurner _{2,

5,

6} , Lock Yue Chew _{7,

8}

Affiliation

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

\sim 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.

中文翻译：

巴厘岛古老的水稻梯田：汉密尔顿方法

我们提出了一种哈密顿方法来重现巴厘岛已有数百年历史的 Subak 灌溉系统的相关元素，显示出稻田斑块的集群大小分布，这是幂律，指数为

～ 2

. 除了这个指数之外，由此产生的系统呈现出两个平衡。第一个源于能量和熵贡献之间的平衡。第二个来自通过局部 Potts 型相互作用与无衰减的远程反铁磁相互作用相结合的特定能量贡献。有限尺寸标度分析表明，作为第二个平衡的结果，Potts（局部铁磁）区域的临界跃迁平衡能量和熵贡献被全局反铁磁相互作用驱动的跃迁吸收，随着系统尺寸的增加. 全局反铁磁区的相变平衡能量和熵贡献也显示出临界迹象。

更新日期：2021-10-14

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