Using an alternative notion of entropy introduced by Datta, the max-entropy, we present a new simplified framework to study the minimizers of the specific free energy for random fields which are weakly dependent in the sense of Lewis, Pfister, and Sullivan. The framework is then applied to derive the variational principle for the loop O ( n ) model and the Ising model in a random percolation environment in the nonmagnetic phase, and we explain how to extend the variational principle to similar models. To demonstrate the generality of the framework, we indicate how to naturally fit into it the variational principle for models with an absolutely summable interaction potential, and for the random-cluster model.

中文翻译：

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弱相关随机场的变分原理

使用 Datta 引入的另一种熵概念，即最大熵，我们提出了一个新的简化框架来研究在 Lewis、Pfister 和 Sullivan 意义上弱依赖的随机场的特定自由能的最小值。然后应用该框架推导出非磁性相中随机渗流环境中环 O ( n ) 模型和 Ising 模型的变分原理，并解释了如何将变分原理扩展到类似模型。为了证明该框架的通用性，我们指出了如何将具有绝对可和相互作用势的模型和随机集群模型的变分原理自然地融入其中。