Related papers: The Primal versus the Dual Ising Model

This chapter provides a general introduction of network modeling in psychometrics. The chapter starts with an introduction to the statistical model formulation of pairwise Markov random fields (PMRF), followed by an introduction of the PMRF…

We obtain a fermionic coset realization of the primaries of minimal unitary models and show how their four-point functions may be calculated by the use of a reduction formula. We illustrate the construction for the Ising model, where we…

We consider a zero-field Ising model defined on a quasiperiodic graph, the so-called Labyrinth tiling. Exact information about the critical behaviour is obtained from duality arguments and the subclass of models which yield commuting…

We study graphical representations for two related models. The first model is the transverse field quantum Ising model, an extension of the original Ising model which was introduced by Lieb, Schultz and Mattis in the 1960's. The second…

We consider a recently introduced generalization of the Ising model in which individual spin strength can vary. The model is intended for analysis of ordering in systems comprising agents which, although matching in their binarity (i.e.,…

We map the problem of finding the prime factors of an integer to the statistical physics problem of finding the ground state of a long-range Ising-like model. As in the strongly disordered Newman-Stein (NS) spin-glass model, the bond…

Causality plays an important role in understanding intelligent behavior, and there is a wealth of literature on mathematical models for causality, most of which is focused on causal graphs. Causal graphs are a powerful tool for a wide range…

Employing heuristic susceptibility equations in conjunction with the well-known critical exponents, the magnetization and partition function for two-dimensional nearest neighbour Ising models are formulated in terms of the Gauss…

It is shown that the partition function of the 2d Ising model on the dual finite lattice with periodical boundary conditions is expressed through some specific combination of the partition functions of the model on the torus with…

The couplings between the Ising model and its graphical representations, the random-cluster, random current and loop $\mathrm{O}(1)$ models, are put on common footing through a generalization of the Swendsen-Wang-Edwards-Sokal coupling. A…

Log-linear models are a classical tool for the analysis of contingency tables. In particular, the subclass of graphical log-linear models provides a general framework for modelling conditional independences. However, with the exception of…

Dynamic scaling analyses are performed in the spin-glass phase of the $\pm J$ Ising, the {\it XY}, and the Heisenberg models in three dimensions. We found a crossover from the critical dynamics to the ground-state dynamics in the Ising…

We revisit the foundations of gauge duality and demonstrate that it can be explained using a modern approach to duality based on a perturbation framework. We therefore put gauge duality and Fenchel-Rockafellar duality on equal footing,…

We prove that the Loop O(1) model, a well-known graphical expansion of the Ising model, is a factor of i.i.d. on unimodular random rooted graphs under various conditions, including in the presence of a non-negative external field. As an…

Gaussian graphical models play an important role in various areas such as genetics, finance, statistical physics and others. They are a powerful modelling tool which allows one to describe the relationships among the variables of interest.…

The one-dimensional transverse field Ising model is solved by continuous unitary transformations in the high-field limit. A high accuracy is reached due to the closure of the relevant algebra of operators which we call string operators. The…

The thermal deformation of the critical point action of the 2D tricritical Ising model gives rise to an exact scattering theory with seven massive excitations based on the exceptional $E_7$ Lie algebra. The high and low temperature phases…

We consider graphs that represent pairwise marginal independencies amongst a set of variables (for instance, the zero entries of a covariance matrix for normal data). We characterize the directed acyclic graphs (DAGs) that faithfully…

Using Monte Carlo simulations we study the two-dimensional Ising model on triangular, square, and hexagonal lattices with various topologies. We focus on the behavior of the magnetic susceptibility and of the specific heat near the critical…

Learning Gibbs distributions using only sufficient statistics has long been recognized as a computationally hard problem. On the other hand, computationally efficient algorithms for learning Gibbs distributions rely on access to full sample…