This paper studies the Yang-Lee edge singularity of 2-dimensional (2D) Ising model through a quantum spin chain. In particular, finite-size scaling measurements on the quantum spin chain are used to determine the low-lying excitation spectrum and central charge at the Yang-Lee edge singularity. The measured values are consistent with predictions for the (A4, A1) minimal conformal field theory. ...

We report on large-scale Wang-Landau Monte Carlo simulations of the critical behavior of two spin models in two(2d) and three-dimensions (3d), namely the 2d random-bond Ising model and the pure 3d Blume-Capel model at zero crystal-field coupling. The numerical data we obtain and the relevant finite-size scaling analysis provide clear answers regarding the universality aspects of both models. In...

We consider the classical duality result of Kramers and Wannier, which expresses the partition function of the twodimensional Ising model at low temperature in terms of the partition function of the two-dimensional Ising model at high temperature. Our main contribution is to gain new insights into this result by reproving it with the help of a simple normalfactor-graph duality theorem (with ori...

We apply the Broad Histogram Method to an Ising system in the context of the recently reformulated Generalized Thermostatistics, and we claim it to be a very efficient simulation tool for this non-extensive statistics. Results are obtained for the nearest-neighbour version of the Ising model for a range of values of the q parameter of Generalized Thermostatistics. We found an evidence that the ...

We discuss a 4-vertex model on an ensemble of 3-valent (Φ) planar random graphs, which has the effect of coupling the vertex model to 2D quantum gravity. The regular lattice equivalent of the model is the symmetric 8-vertex model on the honeycomb lattice, which can be mapped on to an Ising model in field, as was originally shown by Wu et.al. using generalised weak graph transformation technique...

We formulate a cluster Monte Carlo method for the anisotropic limit of Ising models on (d+1)-dimensional lattices, which in effect, are equivalent with d-dimensional quantum transverse Ising models. Using this technique, we investigate the transverse Ising models on the square, triangular, Kagome, honeycomb, and simple-cubic lattices. The Monte Carlo data are analyzed by finite-size scaling. In...

We study the phase diagram of the BCSOS model with an extended interaction range using transfer matrix techniques, pertaining to the (100) surface of single component fcc and bcc crystals. The model shows a 2×2 reconstructed phase and a disordered flat phase. The deconstruction transition between these phases merges with a Kosterlitz-Thouless line, showing an interplay of Ising and Gaussian deg...

The name Ising has come to stand not only for a specific model, but for an entire universality class arguably the most important such class in the theory of critical phenomena. I review several examples, both in and out of equilibrium, in which Ising universality appears or is pertinent. The “Ornstein-Zernike” connection concerns a thermodynamically self-consistent closure of the eponymous rela...

We study the analogy between buckled colloidal monolayers and the triangular-lattice Ising antiferromagnet. We calculate free-volume-induced Ising interactions, show how lattice deformations favor zigzag stripes that partially remove the Ising model ground-state degeneracy, and identify the martensitic mechanism prohibiting perfect stripes. Slowly inflating the spheres yields jamming as well as...

Currently, interactions between voxels are neglected in the tumor control probability (TCP) models used in biologically-driven intensity-modulated radiotherapy treatment planning. However, experimental data suggests that this may not always be justified when bystander effects are important. We propose a model inspired by the Ising model, a short-range interaction model, to investigate if and wh...