相关论文: Exact statistical mechanics of the Ising model on …
Decompositions of networks are useful not only for structural exploration. They also have implications and use in analysis and computational solution of processes (such as the Ising model, percolation, SIR model) running on a given network.…
The Ising model was generalized to a system of cells interacting exclusively by presence of shared spins. Within the cells there are interactions of any complexity, the simplest intracell interactions come down to the Ising model. The…
Recent work on random field Ising model is described briefly emphasizing exact solutions of the model in simple cases and their relevance in understanding equilibrium and non-equilibrium properties of systems with quenched disorder.
We study the equilibrium properties of an Ising model on a disordered random network where the disorder can be quenched or annealed. The network consists of four-fold coordinated sites connected via variable length one-dimensional chains.…
We propose a method for generalizing the Ising model in magnetic fields and calculating the partition function (exact solution) for the Ising model of an arbitrary shape. Specifically, the partition function is calculated using matrices…
Finite size effects for the Ising Model coupled to two dimensional random surfaces are studied by exploiting the exact results from the 2-matrix models. The fixed area partition function is numerically calculated with arbitrary precision by…
A powerful existing technique for evaluating statistical mechanical quantities in two-dimensional Ising models is based on constructing a matrix representing the nearest neighbor spin couplings and then evaluating the Pfaffian of the…
The Ising model is important in statistical modeling and inference in many applications, however its normalizing constant, mean number of active vertices and mean spin interaction -- quantities needed in inference -- are computationally…
Non-equilibrium systems lack an explicit characterisation of their steady state like the Boltzmann distribution for equilibrium systems. This has drastic consequences for the inference of parameters of a model when its dynamics lacks…
Network science provides very powerful tools for extracting information from interacting data. Although recently the unsupervised detection of phases of matter using machine learning has raised significant interest, the full prediction…
We study pairwise Ising models for describing the statistics of multi-neuron spike trains, using data from a simulated cortical network. We explore efficient ways of finding the optimal couplings in these models and examine their…
We study the critical behavior of the Ising model in annealed scale-free (SF) networks of finite system size with forced upper cutoff in degree. By mapping the model onto the weighted fully connected Ising model, we derive analytic results…
While the Ising model remains essential to understand physical phenomena, its natural connection to combinatorial reasoning makes it also one of the best models to probe complex systems in science and engineering. We bring a computational…
The Ising model on an infinite generic tree is defined as a thermodynamic limit of finite systems. A detailed description of the corresponding distribution of infinite spin configurations is given. As an application we study the…
We provide time- and sample-efficient algorithms for learning and testing latent-tree Ising models, i.e. Ising models that may only be observed at their leaf nodes. On the learning side, we obtain efficient algorithms for learning a…
We show that the two dimensional Ising model is complete, in the sense that the partition function of any lattice model on any graph is equal to the partition function of the 2D Ising model with complex coupling. The latter model has all…
Small-world networks provide an interesting framework for studying the interplay between regular and random graphs, where links are located in a regular and random way, respectively. On one hand, the random links make the model to obey some…
A disordered spin glass model where both static and dynamical properties depend on macroscopic magnetizations is presented. These magnetizations interact via random couplings and, therefore, the typical quenched realization of the system…
The Ising model was originally developed to model magnetisation of solids in statistical physics. As a network of binary variables with the probability of becoming 'active' depending only on direct neighbours, the Ising model appears…
The sensitivity of the random field Ising model to small random perturbations of the quenched disorder is studied via exact ground states obtained with a maximum-flow algorithm. In one and two space dimensions we find a mild form of chaos,…