Related papers: Domain statistics in a finite Ising chain
We find the exact critical temperature $T_c$ of the nearest-neighbor ferromagnetic Ising model on an `equilibrium' random graph with an arbitrary degree distribution $P(k)$. We observe an anomalous behavior of the magnetization, magnetic…
We employ a procedure that enables us to calculate the excess free energies for a finite Ising cylinder with domain walls analytically. This procedure transparently covers all possible configurations of the domain walls under given boundary…
A one dimensional network on which there are long range bonds at lattice distances $l>1$ with the probability $P(l) \propto l^{-\delta}$ has been taken under consideration. We investigate the critical behavior of the Ising model on such a…
We study quantum phase transitions in transverse-field Ising spin chains in which the couplings are random but hyperuniform, in the sense that their large-scale fluctuations are suppressed. We construct a one-parameter family of disorder…
We investigate the large-time scaling regimes arising from a variety of metastable structures in a chain of Ising spins with both first- and second-neighbor couplings while subject to a Kawasaki dynamics. Depending on the ratio and sign of…
The local distributions of the one-dimensional dilute annealed Ising model with charged impurities are studied. Explicit expressions are obtained for the pair distribution functions and correlation lengths, and their low-temperature…
We report first principle numerical study of domain wall (DW) depinning in two-dimensional magnetic film, which is modeled by 2D random-field Ising system with the dipole-dipole interaction. We observe nonconventional activation-type motion…
The random motion of a Brownian particle confined in some finite domain is considered. Quite generally, the relevant statistical properties involve infinite series, whose coefficients are related to the eigenvalues of the diffusion…
Domain walls are the topological defects that mediate polarization reversal in ferroelectrics, and they may exhibit quite different geometric and electronic structures compared to the bulk. Therefore, a detailed atomic-scale understanding…
Activated transitions have rates that are often exponentially small in system size. Extracting the associated activation barriers is challenging in practice, especially in the deeply metastable regimes and in the presence of disorder. Here,…
We consider an Ising model on a square grid with ferromagnetic spin-spin interactions spanning beyond nearest neighbors. Starting from initial states with a single unbounded interface separating ordered phases, we investigate the evolution…
Using a recently proposed new renormalization group method (tensor renormalization group), we analyze the Ising model on the 2-dimensional square lattice. For the lowest order approximation with two domain wall states, it realizes the idea…
We study the dynamic and metastable properties of the fully connected Ising $p$-spin model with finite number of variables. We define trapping energies, trapping times and self correlation functions and we analyse their statistical…
We apply extensive Monte Carlo simulations to study the probability distribution $P(m)$ of the order parameter $m$ for the simple cubic Ising model with periodic boundary condition at the transition point. Sampling is performed with the…
Domain walls of a discrete model of an anisotropic ferromagnet are studied. They can be described by sequences of two reversible mappings. Competition between the length scale of spatial structures and the lattice constant leads to a rich…
In this article, we have employed Monte Carlo simulations to study the Ising model on a two-dimensional additive small-world network (A-SWN). The system model consists of a LxL square lattice where each site of the lattice is occupied for a…
We consider testing for the parameters of Ferromagnetic Ising models. While testing for the presence of possibly sparse magnetizations, we provide a general lower bound of minimax separation rates which yields sharp results in high…
The statistics of the ground-state and domain-wall energies for the two-dimensional random-bond Ising model on square lattices with independent, identically distributed bonds of probability $p$ of $J_{ij}= -1$ and $(1-p)$ of $J_{ij}= +1$…
We construct a one-dimensional local spin Hamiltonian with an intrinsically non-local, and therefore anomalous, global $\mathbb{Z}_2$ symmetry. The model is closely related to the quantum Ising model in a transverse magnetic field, and…
We show using extensive simulation results and physical arguments that an Ising system on a two dimensional square lattice, having interactions of random sign between first neighbors and ferromagnetic interactions between second neighbors,…