Related papers: Dynamical Critical Behaviors of the Ising Spin Cha…
We consider an Ising spin-chain in a random transverse magnetic field and compute the zero temperature wave vector and frequency dependent dynamic structure factor numerically by using Jordan-Wigner transformation. Two types of…
We study the low-temperature coarsening of an Ising chain subject to spin-exchange dynamics and a small driving force. This dynamical system reduces to a domain diffusion process, in which entire domains undergo nearest-neighbor hopping,…
Dynamics of Ising models is a much studied phenomenon and has emerged as a rich field of present-day research. An important dynamical feature commonly studied is the quenching phenomenon below the critical temperature. In this thesis we…
After a zero temperature quench, we study the kinetics of the one-dimensional Ising model with long-range interactions between spins at distance $r$ decaying as $r^{-\alpha}$, with $\alpha \le 1$. As shown in our recent study [SciPost Phys…
The random field q-States Potts model is investigated using exact groundstates and finite-temperature transfer matrix calculations. It is found that the domain structure and the Zeeman energy of the domains resembles for general q the…
We investigate the laws of coarsening of a two-dimensional system of Ising spins evolving under single-spin-flip irreversible dynamics at low temperature from a disordered initial condition. The irreversibility of the dynamics comes from…
We study the domain number and size distributions in the one-dimensional Ising and $q$-state Potts models subject to zero-temperature Glauber dynamics. The survival probability of a domain, $S(t)\sim t^{-\psi}$, and an unreacted domain,…
We study the dynamics of an isotropic spin-1/2 Heisenberg chain starting in a domain-wall initial condition, where the spins are initially up on the left half-line and down on the right half-line. We focus on the long-time behavior of the…
If quenched to zero temperature, the one-dimensional Ising spin chain undergoes coarsening, whereby the density of domain walls decays algebraically in time. We show that this coarsening process can be interrupted by exerting a rapidly…
We present a comprehensive study for the statistical properties of random variables that describe the domain structure of a finite Ising chain with nearest-neighbor exchange interactions and free boundary conditions. By use of extensive…
With a nonequilibrium relaxation method, we calculate the dynamic critical exponent z of the two-dimensional Ising model for the Swendsen-Wang and Wolff algorithms. We examine dynamic relaxation processes following a quench from a…
We study the performance of a Wolff-type embedding algorithm for $RP^N$ $\sigma$-models. We find that the algorithm in which we update the embedded Ising model \`a la Swendsen-Wang has critical slowing-down as $z_\chi \approx 1$. If instead…
We study the Swendsen-Wang dynamics for disordered non ferromagnetic Ising models on cubic subsets of the hypercubic lattice Z^d and we show that for all small values of the temperature parameter T the dynamics has a slow relaxation to…
The zero temperature quenching dynamics of the ferromagnetic Ising model on a densely connected small world network is studied where long range bonds are added randomly with a finite probability $p$. We find that in contrast to the sparsely…
We study domain distributions in the one-dimensional Ising model subject to zero-temperature Glauber and Kawasaki dynamics. The survival probability of a domain, $S(t)\sim t^{-\psi}$, and an unreacted domain, $Q_1(t)\sim t^{-\delta}$, are…
The Swendsen-Wang dynamics is a popular algorithm for sampling from the Gibbs distribution for the ferromagnetic Ising model on a graph $G=(V,E)$. The dynamics is a "global" Markov chain which is conjectured to converge to equilibrium in…
We show that the dynamics of an Ising spin chain in a transverse field conserves the number of domains (strings of down spins in an up-spin background) at discrete times. This enables the determination of the eigenfunctions of the…
We study the real-time domain-wall dynamics near a quantum critical point of the one-dimensional anisotropic ferromagnetic spin 1/2 chain. By numerical simulation, we find the domain wall is dynamically stable in the Heisenberg-Ising model.…
Domain walls in the spin S quantum Ising chain at zero temperature are considered. Quantum effects prevent the walls from being sharp and delocalize the exact eigenstates. The absence of a characteristic length of the domain walls is…
Enormous advances have been made in the past 20 years in our understanding of the random-field Ising model, and there is now consensus on many aspects of its behavior at least in thermal equilibrium. In contrast, little is known about its…