Related papers: Gibbs Measures for Long-Range Ising Models
Many modern data sets are sampled with error from complex high-dimensional surfaces. Methods such as tensor product splines or Gaussian processes are effective/well suited for characterizing a surface in two or three dimensions but may…
We report single-cluster Monte Carlo simulations of the Ising model on three-dimensional Poissonian random lattices with up to 128,000 approx. 503 sites which are linked together according to the Voronoi/Delaunay prescription. For each…
Modern large-scale datasets are frequently said to be high-dimensional. However, their data point clouds frequently possess structures, significantly decreasing their intrinsic dimensionality (ID) due to the presence of clusters, points…
A generalization of the compressible Ising model in which spins are hosted on an elastic $D$-dimensional lattice embedded in $d>D$ dimensions is studied. Two critical systems interact when temperature is tuned to the Ising transition point,…
We study parameter inference in large-scale latent variable models. We first propose an unified treatment of online inference for latent variable models from a non-canonical exponential family, and draw explicit links between several…
We give a short non-technical introduction to the Ising model, and review some successes as well as challenges which have emerged from its study in probability and mathematical physics. This includes the infinite-volume theory of phase…
Roughening of interfaces implies the divergence of the interface width $w$ with the system size $L$. For two-dimensional systems the divergence of $w^2$ is linear in $L$. In the framework of a detailed capillary wave approximation and of…
The scaling properties of the wave functions in finite samples of the one dimensional Anderson model are analyzed. The states have been characterized using a new form of the information or entropic length, and compared with analytical…
A two-dimensional Ising model with short-range interactions and mobile defects describing the formation and thermal destruction of defect stripes is studied. In particular, the effect of a local pinning of the defects at the sites of…
We analyze a controversial question about the universality class of the three-dimensional Ising model with long-range-correlated disorder. Whereas both analytical and numerical studies performed so far support an extended Harris criterion…
We review the decay modes of the Standard Model Higgs boson and those of the neutral and charged Higgs particles of the Minimal Supersymmetric extension of the Standard Model. Special emphasis will be put on higher-order effects. [Talk…
This paper considers a non-standard problem of generating samples from a low-temperature Gibbs distribution with \emph{constrained} support, when some of the coordinates of the mode lie on the boundary. These coordinates are referred to as…
We use the single-cluster Monte Carlo update algorithm to simulate the Ising model on two-dimensional Poissonian random lattices of Delaunay type with up to 80\,000 sites. By applying reweighting techniques and finite-size scaling analyses…
The pinning-depinning phase transitions of interfaces for two classes of discrete elastic-string models are investigated numerically. In the (1+1)-dimensions, we revisit these two elastic-string models with slight modification to growth…
The factorization proposal claims that the co-dimension one "pinning defect", on which a local relevant operator is integrated, factorizes the space into two halves in general conformal field theories in the infrared limit. In this letter,…
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…
Networks of interconnected agents are essential to study complex networked systems' state evolution, stability, resilience, and control. Nevertheless, the high dimensionality and nonlinear dynamics are vital factors preventing us from…
The Dyson-Ising ferromagnet is a one-dimensional Ising model with a power law interaction. When the power is between -1 and -2, the model has a phase transition. Van Enter and Le Ny proved that at sufficiently low temperatures the…
The finite-size scaling functions for anisotropic three-dimensional Ising models of size $L_1 \times L_1 \times aL_1$ ($a$: anisotropy parameter) are studied by Monte Carlo simulations. We study the $a$ dependence of finite-size scaling…
While the kinetics of domain growth, even for conserved order-parameter dynamics, is widely studied for short-range inter-particle interactions, systems having long-range interactions are receiving attention only recently. Here we present…