Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userPersistence in One-dimensional Ising Models with Parallel Dynamics
272
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We study persistence in one-dimensional ferromagnetic and anti-ferromagnetic nearest-neighbor Ising models with parallel dynamics. The probability P(t) that a given spin has not flipped up to time t, when the system evolves from an initial random configuration, decays as P(t) sim 1/t^theta_p with theta_p simeq 0.75 numerically. A mapping to the dynamics of two decoupled A+A to 0 models yields theta_p = 3/4 exactly. A finite size scaling analysis clarifies the nature of dynamical scaling in the distribution of persistent sites obtained under this dynamics.
rate research
Read More
In this note we study metastability phenomena for a class of long-range Ising models in one-dimension. We prove that, under suitable general conditions, the configuration -1 is the only metastable state and we estimate the mean exit time. Moreover, we illustrate the theory with two examples (exponentially and polynomially decaying interaction) and we show that the critical droplet can be macroscopic or mesoscopic, according to the value of the external magnetic field.
We study the out-of-equilibrium dynamics of one-dimensional quantum Ising-like systems, arising from sudden quenches of the Hamiltonian parameter $g$ driving quantum transitions between disordered and ordered phases. In particular, we consider quenches to values of $g$ around the critical value $g_c$, and mainly address the question whether, and how, the quantum transition leaves traces in the evolution of the transverse and longitudinal magnetizations during such a deep out-of-equilibrium dynamics. We shed light on the emergence of singularities in the thermodynamic infinite-size limit, likely related to the integrability of the model. Finite systems in periodic and open boundary conditions develop peculiar power-law finite-size scaling laws related to revival phenomena, but apparently unrelated to the quantum transition, because their main features are generally observed in quenches to generic values of $g$. We also investigate the effects of dissipative interactions with an environment, modeled by a Lindblad equation with local decay and pumping dissipation operators within the quadratic fermionic model obtainable by a Jordan-Wigner mapping. Dissipation tends to suppress the main features of the unitary dynamics of closed systems. We finally address the effects of integrability breaking, due to further lattice interactions, such as in anisotropic next-to-nearest neighbor Ising (ANNNI) models. We show that some qualitative features of the post-quench dynamics persist, in particular the different behaviors when quenching to quantum ferromagnetic and paramagnetic phases, and the revival phenomena due to the finite size of the system.
We study the spin-$1/2$ Ising chain with multispin interactions $K$ involving the product of $m$ successive spins, for general values of $m$. Using a change of spin variables the zero-field partition function of a finite chain is obtained for free and periodic boundary conditions (BC) and we calculate the two-spin correlation function. When placed in an external field $H$ the system is shown to be self-dual. Using another change of spin variables the one-dimensional (1D) Ising model with multispin interactions in a field is mapped onto a zero-field rectangular Ising model with first-neighbour interactions $K$ and $H$. The 2D system, with size $mtimes N/m$, has the topology of a cylinder with helical BC. In the thermodynamic limit $N/mtoinfty$, $mtoinfty$, a 2D critical singularity develops on the self-duality line, $sinh 2Ksinh 2H=1$.
Kinetic Ising models on the square lattice with both nearest-neighbor interactions and self-interaction are studied for the cases of random sequential updating and parallel updating. The equilibrium phase diagrams and critical dynamics are studied using Monte Carlo simulations and analytic approximations. The Hamiltonians appearing in the Gibbs distribution describing the equilibrium properties differs for sequential and parallel updating but in both cases feature multispin and non-nearest-neighbor couplings. For parallel updating the system is a probabilistic cellular automaton and the equilibrium distribution satisfies detailed balance with respect to the dynamics [E. N. M. Cirillo, P. Y. Louis, W. M. Ruszel and C. Spitoni, Chaos, Solitons and Fractals, 64:36(2014)]. In the limit of weak self-interaction for parallel dynamics, odd and even sublattices are nearly decoupled and checkerboard patterns are present in the critical and low temperature regimes, leading to singular behavior in the shape of the critical line. For sequential updating the equilibrium Gibbs distribution satisfies global balance but not detailed balance and the Hamiltonian is obtained perturbatively in the limit of weak nearest-neighbor dynamical interactions. In the limit of strong self-interaction the equilibrium properties for both parallel and sequential updating are described by a nearest-neighbor Hamiltonian with twice the interaction strength of the dynamical model.
The dynamics of the one-dimensional random transverse Ising model with both nearest-neighbor (NN) and next-nearest-neighbor (NNN) interactions is studied in the high-temperature limit by the method of recurrence relations. Both the time-dependent transverse correlation function and the corresponding spectral density are calculated for two typical disordered states. We find that for the bimodal disorder the dynamics of the system undergoes a crossover from a collective-mode behavior to a central-peak one and for the Gaussian disorder the dynamics is complex. For both cases, it is found that the central-peak behavior becomes more obvious and the collective-mode behavior becomes weaker as $K_{i}$ increase, especially when $K_{i}>J_{i}/2$ ($J_{i}$ and $K_{i}$ are exchange couplings of the NN and NNN interactions, respectively). However, the effects are small when the NNN interactions are weak ($K_{i}<J_{i}/2$).
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
