With an auxiliary weak external magnetic field, we reexamine the fundamental thermodynamic function, Gibbs free energy $G(T,h)$, to study phase transitions in classical spin lattice models. A cross derivative, i.e., the second-order partial derivative of $G(T,h)$ with respect to both temperature and field, is calculated to precisely locate the critical temperature, which also reveals the nature of a transition. The strategy is efficient and universal, as exemplified by the five-state clock model, two-dimensional (2D) and 3D Ising models, and the $XY$ model, no matter if a transition is trivial or exotic with complex excitations. More importantly, other conjugate pairs could also be integrated into a similar cross derivative if necessary, which would greatly enrich our vision and means to investigate phase transitions both theoretically and experimentally.

中文翻译：

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吉布斯自由能的交叉导数：经典自旋模型中相变的通用有效方法

在辅助弱外部磁场的作用下，我们重新检查了基本的热力学函数吉布斯自由能 $G（Ť，H）$研究经典自旋晶格模型中的相变。交叉导数，即...的二阶偏导数$G（Ť，H）$相对于温度和磁场，可以精确地确定临界温度，这也揭示了过渡的性质。该策略高效且通用，例如五态时钟模型，二维（2D）和3D Ising模型，以及$Xÿ$模型，无论过渡是微不足道的还是复杂的激发。更重要的是，如果需要的话，其他共轭对也可以整合到类似的交叉导数中，这将极大地丰富我们的视野以及研究理论和实验相变的手段。