The existence and limits of metastable droplets have been calculated using finite-system renormalization-group theory, for $q$-state Potts models in spatial dimension $d=3$. The dependence of the droplet critical sizes on magnetic field, temperature, and number of Potts states $q$ has been calculated. The same method has also been used for the calculation of hysteresis loops across first-order phase transitions in these systems. The hysteresis loop sizes and shapes have been deduced as a function of magnetic field, temperature, and number of Potts states $q$. The uneven appearance of asymmetry in the hysteresis loop branches has been noted. The method can be extended to criticality and phase transitions in metastable phases, such as in surface-adsorbed systems and water.

中文翻译：

---

亚稳态Potts小滴

亚稳态液滴的存在和极限已经使用有限系统重归一化群理论进行了计算，对于 $q$维度上的状态Potts模型 $d=3$。液滴临界尺寸对磁场，温度和Potts状态数的依赖性$q$已经计算了。在这些系统中，相同的方法也已用于计算跨越一阶相变的磁滞回线。推导了磁滞回线的大小和形状，它们是磁场，温度和Potts状态数的函数$q$。磁滞回线分支中出现了不对称的不均匀外观。该方法可以扩展到亚稳态相中的临界和相变，例如在表面吸附系统和水中。