Related papers: Long range order for random field Ising and Potts …
Using quantum Monte Carlo simulations and field-theory arguments, we study the fully frustrated (Villain) transverse-field Ising model on the square lattice. We consider a "primary" spin order parameter and a "secondary" dimer order…
In quenched disordered systems, the existence of ordering is generally believed to be only possible in the weak disorder regime (disregarding models of spin-glass type). In particular, sufficiently large random fields is expected to…
We study the ordering kinetics of a generalization of the voter model with long-range interactions, the $p$-voter model, in one dimension. It is defined in terms of boolean variables $S_{i}$, agents or spins, located on sites $i$ of a…
We examine the ordering behavior of the ferromagnetic Ising lattice model defined on a surface with a constant negative curvature. Small-sized ferromagnetic domains are observed to exist at temperatures far greater than the critical…
We study the rate of correlation decay in the two-dimensional random-field Ising model at weak field strength $\varepsilon$. We combine elements of the recent proof of exponential decay of correlations with a quantitative refinement of a…
The sensitivity of the random field Ising model to small random perturbations of the quenched disorder is studied via exact ground states obtained with a maximum-flow algorithm. In one and two space dimensions we find a mild form of chaos,…
The influence of defects of the "random local field" type with an anisotropic distribution of random fields on two-dimensional models with continuous symmetry of the vector order parameter is considered. In the case of weak anisotropy of…
We prove that a class of classical lattice models on $\mathbb{Z}^d$ ($d \geq 2$) with on-site space $\mathbb{N}_0$ and nearest neighbour interaction, exhibits long-range checkerboard order at sufficiently high temperature. The ordering…
The Ising model in a random field and with power-law decaying ferromagnetic bonds is studied at zero temperature. Comparing the scaling of the energy contributions of the ferromagnetic domain wall flip and of the random field a la Imry-Ma…
We study the relaxation of the local ferromagnetic order in the transverse field quantum Ising chain with power-law decaying interactions $1/r^{\alpha}$. We prepare the system in the GHZ state and study the time evolution of the probability…
We give a general condition for a discrete spin system with nearest-neighbor interactions on the $\mathbb{Z}^d$ lattice to exhibit long-range order. The condition is applicable to systems with residual entropy in which the long-range order…
Quasi-one-dimensional antiferromagnetic (AF) quantum spin systems show a wide range of interesting phenomena such as the spin-Peierls transition and disorder driven long range ordering. While there is no magnetic long range order in…
We consider polynomial long-range Ising models in one dimension, with ferromagnetic pair interactions decaying with power $2-\alpha$ (for $0 \leq \alpha < 1$), and prepared with randomly chosen boundary conditions. We show that at low…
An analysis is made of various methods of phenomenological renormalization based on finite-size scaling equations for inverse correlation lengths, the singular part of the free energy density, and their derivatives. The analysis is made…
A rigorous theorem due to Aizenman and Wehr asserts that there can be no latent heat heat in a two-dimensional system with quenched random impurities. We examine this result, and its possible extensions to higher dimensions, in the context…
The one-dimensional Ising model in an external magnetic field with uniform long-range interactions and random short-range interactions satisfying bimodal annealed distributions is studied. This generalizes the random model discussed by…
For the two-dimensional random field Ising model (RFIM) with bimodal (i.e., two-valued) external field, we prove exponential decay of correlations either (1) when the temperature is larger than the critical temperature of the Ising model…
We show by numerical simulations that the correlation function of the random field Ising model (RFIM) in the critical region in three dimensions has very strong fluctuations and that in a finite volume the correlation length is not…
We present asymptotically exact results for the real time order parameter correlations of a class of d=1 Ising models in a transverse field at low temperatures (T) on both sides of the quantum critical point. The correlations are a product…
We have found a simple criterion which allows for the straightforward determination of the order-disorder critical temperatures. The method reproduces exactly results known for the two dimensional Ising, Potts and $Z(N<5)$ models. It also…