论文标题
POTTS模型具有无标度网络上的无形状态
Potts model with invisible states on a scale-free network
论文作者
论文摘要
提出了不同的模型，以通过能量和熵之间的竞争棱镜来理解磁相变。这样的型号之一是带有隐形状态的$ q $ -State Potts模型。该模型引入了$ r $隐形状态，因此，如果旋转位于其中一个，则不会与其余状态相互作用。我们考虑使用无尺度网络上的平均字段近似值的模型，其中具有$ k $度的随机顶点的概率由powerlaw $ p（k）\ propto k^{ - λ} $控制。我们的结果证实，$ q $，$ r $和$λ$扮演影响系统关键行为的全球参数。根据其值，相图分为具有不同临界行为的三个区域。然而，事实证明，由$λ_C（Q）$的边际价值呈现出的拓扑影响在熵影响下是主导的，受无形状态$ r $ $ $ $的影响。
Different models are proposed to understand magnetic phase transitions through the prism of competition between the energy and the entropy. One of such models is a $q$-state Potts model with invisible states. This model introduces $r$ invisible states such that if a spin lies in one of them, it does not interact with the rest states. We consider such a model using the mean field approximation on an annealed scale-free network where the probability of a randomly chosen vertex having a degree $k$ is governed by the power-law $P(k)\propto k^{-λ}$. Our results confirm that $q$, $r$ and $λ$ play a role of global parameters that influence the critical behaviour of the system. Depending on their values, the phase diagram is divided into three regions with different critical behaviours. However, the topological influence, presented by the marginal value of $λ_c(q)$, has proven to be dominant over the entropic influence, governed by the number of invisible states $r$.
