Related papers: Partial inertia induces additional phase transitio…
Recently for a class of critically intermittent random systems a phase transition was found for the finiteness of the absolutely continuous invariant measure. The systems for which this result holds are characterized by the interplay…
We discuss the {\it nonlinear stability} of phase-locked states for globally coupled nonlinear oscillators with finite inertia, namely the modified Kuramoto model, in the context of the robust $\ell^{\infty}$-norm. We show that some classes…
We discuss the short-time behavior of the majority vote dynamics on scale-free networks at the critical threshold. We introduce a heterogeneous mean-field theory on the critical short-time behavior of the majority-vote model on scale-free…
This thesis investigates critical phenomena and equilibrium states in various stochastic models through three interconnected studies. In the first chapter, we analyze the Activated Random Walk model on a one-dimensional ring in the…
We study the synchronized behavior of the inertial Kuramoto oscillators with frustration effect under a symmetric and connected network. Due to the lack of second-order gradient flow structure and singularity of second-order derivative of…
We investigate the collective dynamics of a population of XY model-type oscillators, globally coupled via non-separable interactions that are randomly chosen from a positive or negative value, and subject to thermal noise controlled by…
Discontinuous transitions into absorbing states require an effective mechanism that prevents the stabilization of low density states. They can be found in different systems, such as lattice models or stochastic differential equations (e.g.…
Mixed-order phase transitions display a discontinuity in the order parameter like first-order transitions yet feature critical behavior like second-order transitions. Such transitions have been predicted for a broad range of equilibrium and…
Complex networks often possess communities defined based on network connectivity. When dynamics undergo in a network, one can also consider dynamical communities; i.e., a group of nodes displaying a similar dynamical process. We have…
A new model for the dynamics of opinion formation is proposed and analysed at the mean-field level. It can be regarded as a generalization of the noisy voter model in which agents update their binary states by copying others and by an…
Voting is an important social activity for expressing public opinions. By conceptually considering a group of voting agents to be intelligent matter, the impact of real-time information on voting results is quantitatively studied by an…
We study an entanglement phase transition in a class of chaotic non-Hermitian spin chains whose spin-spin coupling terms commute with the non-Hermitian contributions. Two representative models are investigated: the transverse-field Ising…
Discontinuous quantum phase transitions and the associated metastability play central roles in diverse areas of physics ranging from ferromagnetism to false vacuum decay in the early universe. Using strongly-interacting ultracold atoms in…
Nonequilibrium phase transitions can be typified in a similar way to equilibrium systems, for instance, by the use of the order parameter. However, this characterization hides the irreversible character of the dynamics as well as its…
We investigate the fate of dissipative phase transitions in quantum many-body systems when the individual constituents are qudits ($d$-level systems) instead of qubits. As an example system, we employ a permutation-invariant $XY$ model of…
Discontinuous phase transitions occurs to be particularly interesting from a social point of view because of their relationship to social hysteresis and critical mass. In this paper, we show that the replacement of a time-varying (annealed,…
An infinite-range model of an elastic manifold pulled through a random potential by an applied force $F$ is analyzed focusing on inertial effects. When the inertial parameter, $M$, is small, there is a continuous depinning transition from a…
We propose a new analytical method to study stochastic, binary-state models on complex networks. Moving beyond the usual mean-field theories, this alternative approach is based on the introduction of an annealed approximation for…
A voting model (or a generalization of the Glauber model at zero temperature) on a multidimensional lattice is defined as a system composed of a lattice each site of which is either empty or occupied by a single particle. The reactions of…
In this work we study opinion formation in a population participating of a public debate with two distinct choices. We considered three distinct mechanisms of social interactions and individuals' behavior: conformity, nonconformity and…