The hypergraph offers a platform to study structural properties emerging from more complicated and higher-order than pairwise interactions among constituents and dynamical behavior such as the spread of information or disease. Recently, a simplicial contagion problem was introduced and considered using a simplicial susceptible-infected-susceptible (SIS) model. Although recent studies have investigated random hypergraphs with a Poisson-type facet degree distribution, hypergraphs in the real world can have a power-law type of facet degree distribution. Here, we consider the SIS contagion problem on scale-free uniform hypergraphs and find that a continuous or hybrid epidemic transition occurs when the hub effect is dominant or weak, respectively. We determine the critical exponents analytically and numerically. We discuss the underlying mechanism of the hybrid epidemic transition.

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k-Core percolation has served as a paradigmatic model of discontinuous percolation for a long time. Recently it was revealed that the order parameter of k-core percolation of random networks additionally exhibits critical behavior. Thus k-core percolation exhibits a hybrid phase transition. Unlike the critical behaviors of ordinary percolation that are well understood, those of hybrid percolation transitions have not been thoroughly understood yet. Here, we investigate the critical behavior of k-core percolation of Erdős-Rényi networks. We find numerically that the fluctuations of the order parameter and the mean avalanche size diverge in different ways. Thus, we classify the critical exponents into two types: those associated with the order parameter and those with finite avalanches. The conventional scaling relations hold within each set, however, these two critical exponents are coupled. Finally we discuss some universal features of the critical behaviors of k-core percolation and the cascade failure model on multiplex networks.

We investigate a nonequilibrium phase transition in a dissipative and coherent quantum spin system using the quantum Langevin equation and mean-field theory. Recently, the quantum contact process (QCP) was theoretically investigated using the Rydberg antiblockade effect, in particular, when the Rydberg atoms were excited in s-states so that their interactions were regarded as being between the nearest neighbors. However, when the atoms are excited to d-states, the dipole-dipole interactions become effective, and long-range interactions must be considered. Here, we consider a quantum spin model with a long-range QCP, where the branching and coagulation processes are allowed not only for the nearest-neighbor pairs, but also for long-distance pairs, coherently and incoherently. Using the semiclassical approach, we show that the mean-field phase diagram of our longrange model is similar to that of the nearest-neighbor QCP, where the continuous (discontinuous) transition is found in the weak (strong) quantum regime. However, at the tricritical point, we find a new universality class, which was neither that of the QCP at the tricritical point nor that of the classical directed percolation model with long-range interactions. Implementation of the long-range QCP using interacting cold gases is discussed. arXiv:1901.07682v2 [cond-mat.stat-mech]

Recently, the quantum contact process, in which branching and coagulation processes occur both coherently and incoherently, was theoretically and experimentally investigated in driven open quantum spin systems. In the semi-classical approach, the quantum coherence effect was regarded as a process in which two consecutive atoms are involved in the excitation of a neighboring atom from the inactive (ground) state to the active state (excited s-state). In this case, both second-order and first-order transitions occur. Therefore, a tricritical point exists at which the transition belongs to the tricritical directed percolation (TDP) class. On the other hand, when an atom is excited to the d-state, long-range interaction is induced. Here, to account for this long-range interaction, we extend the TDP model to one with long-range interaction in the form of ∼ 1/r d+σ (denoted as LTDP), where r is the separation, d is the spatial dimension, and σ is a control parameter. In particular, we investigate the properties of the LTDP class below the upper critical dimension d c = min(3, 1.5σ). We numerically obtain a set of critical exponents in the LTDP class and determine the interval of σ for the LTDP class. Finally, we construct a diagram of universality classes in the space (d, σ). arXiv:1911.05964v3 [cond-mat.stat-mech] 31 Jan 2020