The BPS sector of [Formula: see text], [Formula: see text] toric quiver gauge theories, and its corresponding D6-D2-D0 branes on Calabi–Yau threefolds, have been previously studied using integrable lattice models such as the crystal melting model and the dimer model. The asymptotics of the BPS sector, in the large [Formula: see text] limit, can be studied using the Mahler measure theory.[Formula: see text] In this work, we consider the class of isoradial quivers and study their thermodynamic observables and phase structure. Building on our previous results, and using the relation between the Mahler measure and hyperbolic 3-manifolds, we propose a new approach in the asymptotic analysis of the isoradial quivers. As a result, we obtain the observables such as the BPS free energy, the BPS entropy density and growth rate of the isoradial quivers, as a function of the [Formula: see text]-charges of the quiver and in terms of the hyperbolic volumes and the dilogarithm functions. The phase structure of the isoradial quiver is studied via the analysis of the BPS entropy density at critical [Formula: see text]-charges and universal results for the phase structure in this class are obtained. Explicit results for the observables are obtained in some concrete examples of the isoradial quivers.

中文翻译：

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等径向箭袋和双曲 3 流形的热力学

[公式：见正文]、[公式：见正文]复曲面箭袋规范理论的 BPS 部分，及其在 Calabi-Yau 三重上的相应 D6-D2-D0 膜，先前已使用可积晶格模型（例如晶体熔化）进行了研究模型和二聚体模型。BPS 扇区的渐近线，在大 [公式：见文本] 极限，可以使用马勒测度理论来研究。[公式：见文本] 在这项工作中，我们考虑了等径向箭袋的类别，并研究了它们的热力学可观测量和相结构。在我们之前的结果的基础上，利用马勒测度和双曲 3 流形之间的关系，我们提出了一种对等向箭筒进行渐近分析的新方法。因此，我们获得了诸如 BPS 自由能、BPS 熵密度和等径向箭袋的增长率等可观测量值，作为[公式：见正文]-箭袋电荷的函数，并根据双曲线体积和对数函数。通过对临界[公式：见正文]-电荷下的BPS熵密度的分析，研究了等径箭筒的相结构，并获得了该类相结构的普遍结果。在等径向箭袋的一些具体示例中获得了可观察量的明确结果。