Faculty of Physics, Warsaw University of Technology, 00-662 Warsaw, Poland.
Department of Theoretical Physics, Wrocław University of Science and Technology, 50-370 Wrocław, Poland.
Phys Rev E. 2017 Dec;96(6-1):062137. doi: 10.1103/PhysRevE.96.062137. Epub 2017 Dec 26.
We analyze a modified kinetic Ising model, a so-called q-neighbor Ising model, with Metropolis dynamics [Phys. Rev. E 92, 052105 (2015)PLEEE81539-375510.1103/PhysRevE.92.052105] on a duplex clique and a partially duplex clique. In the q-neighbor Ising model each spin interacts only with q spins randomly chosen from its whole neighborhood. In the case of a duplex clique the change of a spin is allowed only if both levels simultaneously induce this change. Due to the mean-field-like nature of the model we are able to derive the analytic form of transition probabilities and solve the corresponding master equation. The existence of the second level changes dramatically the character of the phase transition. In the case of the monoplex clique, the q-neighbor Ising model exhibits a continuous phase transition for q=3, discontinuous phase transition for q≥4, and for q=1 and q=2 the phase transition is not observed. On the other hand, in the case of the duplex clique continuous phase transitions are observed for all values of q, even for q=1 and q=2. Subsequently we introduce a partially duplex clique, parametrized by r∈[0,1], which allows us to tune the network from monoplex (r=0) to duplex (r=1). Such a generalized topology, in which a fraction r of all nodes appear on both levels, allows us to obtain the critical value of r=r^{*}(q) at which a tricriticality (switch from continuous to discontinuous phase transition) appears.
我们分析了一个修正的动力学伊辛模型，即所谓的 q-邻居伊辛模型，采用 Metropolis 动力学[Phys. Rev. E 92, 052105 (2015)PLEEE81539-375510.1103/PhysRevE.92.052105]，在双链形团簇和部分双链形团簇上。在 q-邻居伊辛模型中，每个自旋仅与从整个近邻中随机选择的 q 个自旋相互作用。在双链形团簇的情况下，只有当两个能级同时诱导这种变化时，才允许自旋发生变化。由于模型具有类平均场的性质，我们能够推导出跃迁概率的解析形式，并求解相应的主方程。第二能级的存在极大地改变了相变的性质。在单链团簇的情况下，q-邻居伊辛模型对于 q=3 表现出连续相变，对于 q≥4 表现出不连续相变，而对于 q=1 和 q=2 则观察不到相变。另一方面，在双链形团簇的情况下，对于所有 q 值都观察到连续相变，甚至对于 q=1 和 q=2 也是如此。随后，我们引入了部分双链形团簇，由 r∈[0,1]参数化，这允许我们调整网络从单链（r=0）到双链（r=1）。这种广义拓扑结构，其中一部分 r 的所有节点都出现在两个能级上，允许我们获得 r=r*(q)的临界值，在该值处出现三临界点（从连续到不连续相变的转变）。
