Related papers: The $Z$-invariant Ising model via dimers
The Ising-Kac model is a variant of the ferromagnetic Ising model in which each spin variable interacts with all spins in a neighbourhood of radius $\gamma^{-1}$ for $\gamma \ll 1$ around its base point. We study the Glauber dynamics for…
We describe numerical simulations of the stochastic diffusion equation with a conserved charge. We focus on the dynamics in the vicinity of a critical point in the Ising universality class. The model we consider is expected to describe the…
Topological quantum state described by the global invariant has been extensively studied in theory and experiment. In this letter, we investigate the relationship between \emph{Zitterbewegung} and the topology of systems that reflect the…
The XOR-Ising model on a graph consists of random spin configurations on vertices of the graph obtained by taking the product at each vertex of the spins of two independent Ising models. In this paper, we explicitly relate loop…
The Casimir effect for a massless scalar field with Dirichlet and periodic boundary conditions (b.c.) on infinite parallel plates is revisited in the local quantum field theory (lqft) framework introduced by B.Kay. The model displays a…
In this paper, we prove a general result concerning finite-range, attractive interacting particle systems on $\{-1, 1\}^{\mathbb{Z}^d}$. If the particle system has a unique stationary measure and, in a precise sense, relaxes to this…
We study the dynamical response of a two-dimensional Ising model subject to a square-wave oscillating external field. In contrast to earlier studies, the system evolves under a so-called soft Glauber dynamic [P.A. Rikvold and M. Kolesik, J.…
The paper considers the generalized Ising model in the $2\times2\times\infty$ strip with a Hamiltonian invariant with respect to the central axis of rotation through the angle $\pi/2$, which includes all possible multiplicative interactions…
Consider the natural graph associated to a rhombus tiling of a polygonal regionin the plane. The spin correlations between boundary vertices of this graph inthe Z-invariant Ising model do not depend on the choice of the rhombus tilingbut…
The applicability of the Lifshitz formula is discussed to the case of two thick parallel plates made of real metal. The usual description of the zero-point vacuum oscillations on the background of the frequency-dependent dielectric…
We prove that the marginal densities of a global probability mass function in a primal normal factor graph and the corresponding marginal densities in the dual normal factor graph are related via local mappings. The mapping depends on the…
We consider an Ising model on the Cayley tree $\Gamma_k$ of arbitrary order $k\ge1$ with three spin species of values $(\tfrac12,1,\tfrac32)$ distributed deterministically with period three along the generations. Within the framework of…
We have substantially extended the high-temperature and low-magnetic-field (and the related low-temperature and high-magnetic-field) bivariate expansions of the free energy for the conventional three-dimensional Ising model and for a…
We prove an optimal $O(n \log n)$ mixing time of the Glauber dynamics for the Ising models with edge activity $\beta \in \left(\frac{\Delta-2}{\Delta}, \frac{\Delta}{\Delta-2}\right)$. This mixing time bound holds even if the maximum degree…
We investigate the dynamic critical exponent of the two-dimensional Ising model defined on a curved surface with constant negative curvature. By using the short-time relaxation method, we find a quantitative alteration of the dynamic…
There is proposed a model of scale-free random graphs which are locally close to the uncorrelated complex random networks with divergent $\langle k^2 \rangle$ studied in e.g. S. N. Dorogovtsev {\it et al}, Rev. Mod. Phys. {\bf 80}, 1275…
We study purely dissipative relaxational dynamics in the three-dimensional Ising universality class. To this end, we simulate the improved Blume-Capel model on the simple cubic lattice by using local algorithms. We perform a finite size…
We present a systematic method to calculate the universal scaling functions for the critical Casimir force and the according potential of the two-dimensional Ising model with various boundary conditions. Therefore we start with the dimer…
We construct explicit jointly invariant measures for the periodic KPZ equation (and therefore also the stochastic Burgers' and stochastic heat equations) for general slope parameters and prove their uniqueness via a one force--one solution…
We study the zero-temperature stochastic Ising model on some connected planar quasi-transitive graphs, which are invariant under rotation and translation. The initial spin configuration is distributed according to a Bernoulli product…