We investigate a new class of [Formula: see text]-dimensional topological black hole solutions in the context of massive gravity and in the presence of logarithmic nonlinear electrodynamics. Exploring higher-dimensional solutions in massive gravity coupled to nonlinear electrodynamics is motivated by holographic hypothesis as well as string theory. We first construct exact solutions of the field equations and then explore the behavior of the metric functions for different values of the model parameters. We observe that our black holes admit the multi-horizons caused by a quantum effect called anti-evaporation. Next, by calculating the conserved and thermodynamic quantities, we obtain a generalized Smarr formula. We find that the first law of black holes thermodynamics is satisfied on the black hole horizon. We study thermal stability of the obtained solutions in both canonical and grand canonical ensembles. We reveal that depending on the model parameters, our solutions exhibit a rich variety of phase structures. Finally, we explore, for the first time without extending thermodynamics phase space, the critical behavior and reentrant phase transition for black hole solutions in massive gravity theory. We realize that there is a zeroth-order phase transition for a specified range of charge value and the system experiences a large/small/large reentrant phase transition due to the presence of nonlinear electrodynamics.

中文翻译：

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大质量重力对数非线性带电黑洞的热力学和重入相变

我们在大质量重力和对数非线性电动力学存在的情况下研究了一类新的[公式：见文本]维拓扑黑洞解。在全息假设和弦理论的推动下，探索与非线性电动力学耦合的大质量重力的高维解。我们首先构造场方程的精确解，然后探索不同模型参数值的度量函数的行为。我们观察到我们的黑洞承认由称为反蒸发的量子效应引起的多视界。接下来，通过计算守恒量和热力学量，我们得到了一个广义的 Smarr 公式。我们发现黑洞热力学第一定律在黑洞视界上得到满足。我们研究了规范和大规范合奏中获得的解决方案的热稳定性。我们揭示，根据模型参数，我们的解决方案表现出丰富多样的相结构。最后，我们首次在不扩展热力学相空间的情况下探索了大质量引力理论中黑洞解的临界行为和重入相变。我们意识到对于指定的电荷值范围存在零阶相变，并且由于非线性电动力学的存在，系统经历了大/小/大的重入相变。首次在不扩展热力学相空间的情况下，研究了大质量引力理论中黑洞解的临界行为和重入相变。我们意识到对于指定的电荷值范围存在零阶相变，并且由于非线性电动力学的存在，系统经历了大/小/大的重入相变。首次在不扩展热力学相空间的情况下，研究了大质量引力理论中黑洞解的临界行为和重入相变。我们意识到对于指定的电荷值范围存在零阶相变，并且由于非线性电动力学的存在，系统经历了大/小/大的重入相变。