论文标题
解决3D ISING模型需要什么？有效解决方案的最小必要条件
What does it take to solve the 3D Ising model? Minimal necessary conditions for a valid solution
论文作者
论文摘要
Ising模型在简单的立方晶格上的精确解决方案是严格统计力学中的长期开放问题之一。确实，人们普遍认为，定居将构成方法论的突破，促进进一步应用的巨大前景，类似于Lars Onsager在八十年前解决二维模型时发生的事情。因此，已经有许多尝试找到确切分区函数$ z $的分析表达式，但是由于不可避免的概念或数学障碍，所有此类尝试都失败了。鉴于这种简单但范式模型的重要性，在这里，我们列出了$ z $的任何声称的确切表达式的明确标准，以使其最小化。具体来说，我们提出了$ z $必须满足的六个必要条件（但不够）。这些标准将允许对未来索赔进行非常快速的合理性检查。作为说明性的例子，我们讨论了以前的错误``解决方案''，揭示了他们的缺点。
Exact solution of the Ising model on the simple cubic lattice is one of the long-standing open problems in rigorous statistical mechanics. Indeed, it is generally believed that settling it would constitute a methodological breakthrough, fomenting great prospects for further application, similarly to what happened when Lars Onsager solved the two dimensional model eighty years ago. Hence, there have been many attempts to find analytic expressions for the exact partition function $Z$, but all such attempts have failed due to unavoidable conceptual or mathematical obstructions. Given the importance of this simple yet paradigmatic model, here we set out clear-cut criteria for any claimed exact expression for $Z$ to be minimally plausible. Specifically, we present six necessary -- but not sufficient -- conditions that $Z$ must satisfy. These criteria will allow very quick plausibility checks of future claims. As illustrative examples, we discuss previous mistaken ``solutions,'' unveiling their shortcomings.
