Related papers: Exponential decay of correlations in the two-dimen…
A periodic Ising model is one endowed with interactions that are invariant under translations of members of a full-rank sublattice $\mathfrak{L}$ of $\mathbb{Z}^2$. We give an exact, quantitative description of the critical temperature,…
We examine the Ising model at its critical temperature with an external magnetic field $h a^{\frac{15}{8}}$ on $a\mathbb{Z}^2$ for $a,h >0$. A new proof of exponential decay of the truncated two-point correlation functions is presented. It…
Magnetization switching in highly anisotropic single-domain ferromagnets has been previously shown to be qualitatively described by the droplet theory of metastable decay and simulations of two-dimensional kinetic Ising systems with…
The dynamics of a random (quenched) field Ising model (in two dimension) at zero temperature in the presence of an additional sinusoidally oscillating homogeneous (in space) magnetic field has been studied by Monte Carlo simulation using…
The four dimensional Gaussian random field Ising magnet is investigated numerically at zero temperature, using samples up to size $64^4$, to test scaling theories and to investigate the nature of domain walls and the thermodynamic limit. As…
For the Ising model defined on $a\mathbb{Z}^2$ at critical temperature with external field $a^{15/8}h$, we give a simple and elementary proof that its truncated two-point function decays exponentially. The proof combines the high…
We solve the growing asymmetric Ising model [Phys. Rev. E 89, 012105 (2014)] in the topologies of deterministic and stochastic (random) scale-free trees predicting its non-monotonous behavior for external fields smaller than the coupling…
We investigate the final state of zero-temperature Ising ferromagnets which are endowed with single-spin flip Glauber dynamics. Surprisingly, the ground state is generally not reached for zero initial magnetization. In two dimensions, the…
High-dimensional ($d\ge 5$) Ising systems have mean-field critical exponents. However, at the critical temperature the finite-size scaling of the susceptibility $\chi$ depends on the boundary conditions. A system with periodic boundary…
The nature of the zero temperature ordering transition in the 3D Gaussian random field Ising magnet is studied numerically, aided by scaling analyses. In the ferromagnetic phase the scaling of the roughness of the domain walls, $w\sim…
The one-dimensional Ising model is easily generalized to a \textit{genuinely nonequilibrium} system by coupling alternating spins to two thermal baths at different temperatures. Here, we investigate the full time dependence of this system.…
We investigate the zero-temperature quantum phase transition of the random bond Ising chain in a transverse magnetic field. Its critical properties are identical to those of the McCoy-Wu model, which is a classical Ising model in two…
Transfer-matrix methods are used to calculate spin-spin correlation functions ($G$), Helmholtz free energies ($f$) and magnetizations ($m$) in the two-dimensional random-field Ising model close to the zero-field bulk critical temperature…
We investigate the low-temperature critical behavior of the three dimensional random-field Ising ferromagnet. By a scaling analysis we find that in the limit of temperature $T \to 0$ the usual scaling relations have to be modified as far as…
The ferromagnetic transition in the Ising model is the paradigmatic example of ergodicity breaking accompanied by symmetry breaking. It is routinely assumed that the thermodynamic limit is taken with free or periodic boundary conditions.…
We study the zero-temperature behavior of the infinite-ranged Ising spin glass in a transverse field. Using spin summation techniques and Monte Carlo methods we characterize the zero-temperature quantum transition. Our results are well…
The exact determination of ground states of small systems is used in a scaling study of the random-field Ising model. While three variants of the model are found to be in the same universality class in 3 dimensions, the Gaussian and bimodal…
We study finite temperature properties of metals close to an Ising-nematic quantum critical point in two spatial dimensions. In particular we show that at any finite temperature there is a regime where order parameter fluctuations are…
We present numerical simulations of the random field Ising model in three dimensions at zero temperature. The critical exponents are found to agree with previous results. We study the magnetic susceptibility by applying a small magnetic…
We consider the random-anisotropy model on the square and on the cubic lattice in the strong-anisotropy limit. We compute exact ground-state configurations, and we use them to determine the stiffness exponent at zero temperature; we find…