Related papers: Emergent behaviors of Thermodynamic Kuramoto ensem…
We present a collective coordinate approach to describe coupled phase oscillators. We apply the method to study synchronisation in a Kuramoto model. In our approach an N-dimensional Kuramoto model is reduced to an n-dimensional ordinary…
We use high-temperature series expansions to obtain thermodynamic properties of the quantum compass model, and to investigate the phase transition on the square and simple cubic lattices. On the square lattice we obtain evidence for a phase…
The Kuramoto model was recently extended to arbitrary dimensions by reinterpreting the oscillators as particles moving on the surface of unit spheres in a D-dimensional space. Each particle is then represented by a D-dimensional unit…
We study dynamics of populations of resonantly coupled oscillators having different frequencies. Starting from the coupled van der Pol equations we derive the Kuramoto-type phase model for the situation, where the natural frequencies of two…
Solitary states emerge in oscillator networks when one oscillator separates from the fully synchronized cluster and becomes incoherent with the rest of the network. Such chimera-type patterns with an incoherent state formed by a single…
We present a comprehensive study of the thermodynamic properties of the three-dimensional fermionic Hubbard model, with application to cold fermionic atoms subject to an optical lattice and a trapping potential. Our study is focused on the…
Magnetic and electronic states of an Ising-spin Kondo lattice model on a kagome lattice are investigated by a Monte Carlo simulation. In addition to the conventional ferromagnetic and ferrimagnetic orders, we show that this model exhibits…
Engineering new quantum phases requires fine tuning of the electronic, orbital, spin, and lattice degrees of freedom. To this end, the kagome lattice with flat bands has garnered great attention by hosting various topological and correlated…
We study the emergence of synchronization in the Kuramoto model on a digraph in the presence of time delays. Assuming the digraph is strongly connected, we first establish a uniform bound on the phase diameter and subsequently prove the…
Phase diagram of an Ising-spin Kondo lattice model on a kagome lattice is investigated by a Monte Carlo simulation. We find that the system exhibits a peculiar ferrimagnetic state at a finite temperature, in which each triangle is in a…
We present constants of motion for the finite-dimensional Lohe type aggregation models with frustration and we apply them to analyze the emergence of collective behaviors. The Lohe type models have been proposed as possible non-abelian and…
We propose a thermodynamic multi-state spin model in order to describe equilibrial behavior of a society. Our model is inspired by the Axelrod model used in social network studies. In the framework of the statistical mechanics language, we…
We perform extensive Monte Carlo simulations to investigate the dynamic phase transition properties of the two-dimensional kinetic Ising model on the kagome lattice in the presence of square-wave oscillating magnetic field. Through detailed…
We consider a two dimensional Kondo lattice model with exchange J and hopping t in which three out of four impurity spins are removed in a regular way. At the particle-hole symmetric point the model may be studied with auxiliary field…
The entrainment transition of coupled random frequency oscillators presents a long-standing problem in nonlinear physics. The onset of entrainment in populations of large but finite size exhibits strong sensitivity to fluctuations in the…
We study the synchronization physics of 1D and 2D oscillator lattices subject to noise and predict a dynamical transition that leads to a sudden drastic increase of phase diffusion. Our analysis is based on the widely applicable…
The Kuramoto model, a paradigmatic framework for studying synchronization, exhibits a transition to collective oscillations only above a critical coupling strength in the thermodynamic limit. However, real-world systems are finite, and…
We analyze repulsively coupled Kuramoto oscillators, which are exposed to a distribution of natural frequencies. This source of disorder leads to closed orbits with a variety of different periods, which can be orders of magnitude longer…
The temperature-dependent evolution of the Kondo lattice is a long-standing topic of theoretical and experimental investigation and yet it lacks a truly microscopic description of the relation of the basic $f$-$d$ hybridization processes to…
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…