Related papers: Scaling laws and relaxation rate at desynchronizat…
A coupled phase-oscillator model consists of phase-oscillators, each of which has the natural frequency obeying a probability distribution and couples with other oscillators through a given periodic coupling function. This type of model is…
We study the effect of structured higher-order interactions on the collective behavior of coupled phase oscillators. By combining a hypergraph generative model with dimensionality reduction techniques, we obtain a reduced system of…
Critical slowing down of the relaxation of the order parameter is relevant both in early the universe and in ultrarelativistic heavy ion collisions. We study the relaxation rate of the order parameter in an O(N) scalar theory near the…
We consider the contact process near an extended surface defect, where the local control parameter deviates from the bulk one by an amount of $\lambda(l)-\lambda(\infty) = A l^{-s}$, $l$ being the distance from the surface. We concentrate…
The accurate estimation of scaling exponents is central in the observational study of scale-invariant phenomena. Natural systems unavoidably provide observations over restricted intervals; consequently a stationary stochastic process (time…
Phenomenological scaling arguments suggest the existence of universal amplitudes in the finite-size scaling of certain correlation lengths in strongly anisotropic or dynamical phase transitions. For equilibrium systems, provided that…
Coupled oscillator networks often display transitions between qualitatively different phase-locked solutions -- such as synchrony and rotating wave solutions -- following perturbation or parameter variation. In the limit of weak coupling,…
The finite-size scaling theory for continuous phase transition plays an important role in determining critical point and critical exponents from the size-dependent behaviors of quantities in the thermodynamic limit. For percolation phase…
We investigate the off-equilibrium dynamics of a classical spin system with $O(n)$ symmetry in $2< D <4$ spatial dimensions and in the limit $n\to \infty$. The system is set up in an ordered equilibrium state is and subsequently driven out…
We report a quantum Monte Carlo study of the phase transition between antiferromagnetic and valence-bond solid ground states in the square-lattice $S=1/2$ $J$-$Q$ model. The critical correlation function of the $Q$ terms gives a scaling…
We investigate the equilibrium and off-equilibrium behaviors of systems at thermal first-order transitions (FOTs) when the boundary conditions favor one of the two phases. As a theoretical laboratory we consider the two-dimensional Potts…
We investigate collective synchronization in a system of coupled oscillators on small-world networks. The order parameters which measure synchronization of phases and frequencies are introduced and analyzed by means of dynamic simulations…
We demonstrate the emergence of self-organized structures in the course of the relaxation of an initially excited, dissipative and finite chain of interacting particles in a periodic potential towards its many particle equilibrium…
In the modern theory of polarization, polarization itself is given by a geometric phase. In calculations for interacting systems the polarization and its variance are obtained from the polarization amplitude. We interpret this quantity as a…
We discuss the universal scaling laws of order parameter fluctuations in any system in which the second-order critical behaviour can be identified. These scaling laws can be derived rigorously for equilibrium systems when combined with the…
We propose a novel finite size scaling analysis for percolation transition observed in complex networks. While it is known that cooperative systems in growing networks often undergo an infinite order transition with inverted…
Interspersing unitary dynamics with local measurements results in measurement-induced phases and transitions in many-body quantum systems. When the evolution is driven by a local Hamiltonian, two types of transitions have been observed,…
The jamming transition of particles with finite-range interactions is characterized by a variety of critical phenomena, including power law distributions of marginal contacts. We numerically study a recently proposed simple model of…
First-order phase transitions, classical or quantum, subject to randomness coupled to energy-like variables (bond randomness) can be rounded, resulting in continuous transitions (emergent criticality). We study perhaps the simplest such…
We carry out a finite size scaling analysis of the jamming transition in frictionless bi-disperse soft core disks in two dimensions. We consider two different jamming protocols: (i) quench from random initial positions, and (ii) quasistatic…