不连续的过渡已经收到了相当大的兴趣，由于发现，许多现象，如灾难性的变化，流行病爆发和同步呈现的行为签署的突然（宏观）的变化（而不是平滑的）作为一个调整参数的变化。然而，在不同的情况下，仍然缺乏再现上述商标的微观模型。考虑到这些想法，我们研究了最近在[Phys. Rev. E { \bf 95}，042304（2017）]中确定的具有上下$Z_2$对称性的最简单系统之一中支撑不连续跃迁的基本成分。在复杂网络中，由于惯性这一额外因素的存在，系统的连续过渡被切换为不连续过渡。我们仔细研究三个基本成分的作用：惯性，系统度，和晶格拓扑结构。我们的分析已经进行了规则格和随机规则网络与不同的节点度（相互作用的邻域），通过平均场处理和数值模拟。我们的研究结果表明，不仅惯性，而且连接构成的基本要素，为转移的相变。令人惊讶的是，它们也表现在低维规则拓扑中，暴露出与复杂网络情况完全不同的缩放行为。因此，我们的研究结果提出了坚实的基础上的不连续过渡的表现形式，在这样的相关类系统与$Z_2$对称性的基本问题。
英文摘要：
Discontinuous transitions have received considerable interest due to the uncovering that many phenomena such as catastrophic changes, epidemic outbreaks and synchronization present a behavior signed by abrupt (macroscopic) changes (instead of smooth ones) as a tuning parameter is changed. However, in different cases there are still scarce microscopic models reproducing such above trademarks. With these ideas in mind, we investigate the fundamental ingredients underpinning the discontinuous transition in one of the simplest systems with up-down $Z_2$ symmetry recently ascertained in [Phys. Rev. E {\bf 95}, 042304 (2017)]. Such system, in the presence of an extra ingredient-the inertia- has its continuous transition being switched to a discontinuous one in complex networks. We scrutinize the role of three fundamental ingredients: inertia, system degree, and the lattice topology. Our analysis has been carried out for regular lattices and random regular networks with different node degrees (interacting neighborhood) through mean-field treatment and numerical simulations. Our findings reveal that not only the inertia but also the connectivity constitute essential elements for shifting the phase transition. Astoundingly, they also manifest in low-dimensional regular topologies, exposing a scaling behavior entirely different than those from the complex networks case. Therefore, our findings put on firmer bases the essential issues for the manifestation of discontinuous transitions in such relevant class of systems with $Z_2$ symmetry.
Partial inertia induces additional phase transition in the explosive majority vote model
近年来，人们对炸药（即，不连续的）过渡。它们表现在不同的系统中，如耦合振子的同步，渗流制度，吸收相变和最近，在多数表决（MV）模型与惯性。在后者中，模型规则通过包含取决于局部自旋的项（惯性项）而略有修改。在这种情况下，Chen等人（Phys Rev. E {5}，042304（2017））发现，相关惯性改变了复杂网络中相变的性质，从连续到不连续。在这里，我们给出了一个进一步的步骤，通过嵌入惯性只在顶点的度大于阈值$\langle k \rangle k^*$，$\langle k \rangle$是平均系统度和$k^*$分数限制。我们的结果，从平均场分析和广泛的数值模拟，揭示了一个爆炸性的转变，在均匀和非均匀结构的小和中等$k^*$的。否则，大的限制只能在异质情况下维持不连续的过渡。这与Kuramoto模型的最近结果（Phys Rev. E {91}，022818（2015））具有一些相似性。令人惊讶的是，中间的限制和大的惯性是负责的额外相的出现，其中系统是部分同步的和相变的分类取决于惯性和晶格拓扑结构。在这种情况下，系统表现出两个相变。
