Probabilistic model checking is an emerging verification technology for probabilistic analysis. Its use has been started not only in computer science but also in interdisciplinary fields. In this paper, we show that probabilistic model checking allows one to analyze the magnetic behaviors of the one-dimensional Ising model, which describes physical phenomena of magnets. The Ising model consists...

The framework is presented of Bayesian image restoration for multivalued images by means of the Q-Ising model with nearest-neighbor interactions. Hyperparameters in the probabilistic model are determined so as to maximize the marginal likelihood. A practical algorithm is described for multi-valued image restoration based on the Bethe approximation. The algorithm corresponds to loopy belief prop...

In the paper the Ising model with competing J1 and J2 interactions with spin values ±1, on a Cayley tree of order 2 (with 3 neighbors) is considered . We study the structure of the ground states and verify the Peierls condition for the model. Our second result gives description of Gibbs measures for ferromagnetic Ising model with J1 < 0 and J2 = 0, using a contour argument which we also develop...

We consider the ferromagnetic Ising model on a sequence of graphs Gn converging locally weakly to a rooted random tree. Generalizing [Probab. Theory Related Fields 152 (2012) 31–51], under an appropriate “continuity” property, we show that the Ising measures on these graphs converge locally weakly to a measure, which is obtained by first picking a random tree, and then the symmetric mixture of ...

We restudy the phase diagram of the 2D-Ising model with competing interactions J1 on nearest neighbour and J2 on next-nearest neighbour bonds via Monte-Carlo simulations. We present the finite temperature phase diagram and introduce computational methods which allow us to calculate transition temperatures close to the critical point at J2 = 0.5J1. Further on we investigate the character of the ...

We present an efficient algorithm for calculating the properties of Ising models in two dimensions, directly in the spin basis, without the need for mapping to fermion or dimer models. The algorithm computes the partition function and correlation functions at a single temperature on any planar network of N Ising spins in O(N;{3/2}) time or less. The method can handle continuous or discrete bond...

Properties of magnetic films are studied in the framework of Ising models. In particular, we discuss critical phenomena of ferromagnetic Ising films with straight lines of magnetic adatoms and straight steps on the surface as well as phase diagrams of the axial next–nearest neighbour Ising (ANNNI) model for thin films exhibiting various spatially modulated phases.

The quantization of a free boson whose momentum satisfies a cubic constraint leads to a c = 1 2 conformal field theory with a BRST symmetry. The theory also has a W∞ symmetry in which all the generators except the stress-tensor are BRST-exact and so topological. The BRST cohomology includes states of conformal dimensions 0, 1 16 , 1 2 , together with ‘copies’ of these states obtained by acting ...

(1) Exact universal amplitude ratios for two-dimensional Ising model and a quantum spin chain. (2) Critical behaviour of semi-infinite quenched dilute Ising-like systems in three dimensions: Ordinary transition. (3) Universal scaling functions for bond percolation on planar random and square lattices with multiple percolating clusters. (4) Polydispersity effect and universality of finite-size s...

One outstanding unsolved problem in statistical mechanics is the closedform computation of the free energy of the two-dimensional Ising model in a nonzero magnetic field. In 1976 Verhagen (1~ considered one particular triangular Ising model, and obtained its solution along a certain trajectory in the parameter space. This solution, which was obtained through the consideration of a stochastic cr...