Related papers: Small-correlation expansions for the inverse Ising…
The exact solution of a two-dimensional (2D) Ising model with the next nearest interactions at zero magnetic field is derived. At first, the transfer matrices are analyzed in three representations, i.e., Clifford algebraic representation,…
An extended ensemble Monte Carlo algorithm is proposed by introducing a violation of the detailed balance condition to the update scheme of the inverse temperature in simulated tempering. Our method, irreversible simulated tempering, is…
Interdependence is a fundamental ingredient to analyze the stability of many real-world complex systems featuring functional liasons. Yet, physical realizations of this coupling are still unknown, due to the lack of a theoretical framework…
The two-dimensional Ising model is the simplest model of statistical mechanics exhibiting a second order phase transition. While in absence of magnetic field it is known to be solvable on the lattice since Onsager's work of the forties,…
We study long-range correlation functions of the rectangular Ising lattice with cyclic boundary conditions. Specifically, we consider the situation in which two spins are on the same column, and at least one spin is on or near free…
We obtain an exact solution for a generalized three-chain Ising tube (TCGIT) of length $L$ with toroidal boundary conditions and the most general $C_3$-invariant Hamiltonian on an elementary prism, containing 20 independent coupling…
25th-order high-temperature series are computed for a general nearest-neighbor three-dimensional Ising model with arbitrary potential on the simple cubic lattice. In particular, we consider three improved potentials characterized by…
The statistics of critical spin-spin correlation functions in Ising systems with non-frustrated disorder are investigated on a strip geometry, via numerical transfer-matrix techniques. Conformal invariance concepts are used, in order to…
An analysis is made of various methods of phenomenological renormalization based on finite-size scaling equations for inverse correlation lengths, the singular part of the free energy density, and their derivatives. The analysis is made…
Reducing a graph while preserving its overall properties is an important problem with many applications. Typically, reduction approaches either remove edges (sparsification) or merge nodes (coarsening) in an unsupervised way with no…
We compute the combined two and three loop order correction to the spin-spin correlation functions for the 2D Ising and q-states Potts model with random bonds at the critical point. The procedure employed is the renormalisation group…
The common feature for a nontrivial hard problem is the existence of nontrivial topological structures, non-planarity graphs, nonlocalities, or long-range spin entanglements in a model system with randomness. For instance, the Boolean…
The magnetic systems with disorder form an important class of systems, which are under intensive studies, since they reflect real systems. Such a class of systems is the spin glass one, which combines randomness and frustration. The…
The Fortuin-Kasteleyn mapping between the Ising model and the site-bond correlated percolation model is shown to be only one of an infinite class of exact mappings. These new cluster representations are a result of "renormalized"…
The inverse renormalization group is studied based on the image super-resolution using the deep convolutional neural networks. We consider the improved correlation configuration instead of spin configuration for the spin models, such as the…
We consider spin-spin correlation functions for spins along a row, $R_n = \langle \sigma_{0,0}\sigma_{n,0}\rangle$, in the two-dimensional Ising model. We discuss a method for calculating general-$n$ expressions for coefficients in…
Based on the connection between the Ising model and a correlated percolation model, we calculate the distribution function for the fraction ($c$) of lattice sites in percolating clusters in subgraphs with $n$ percolating clusters, $f_n(c)$,…
Determining the phase diagram of systems consisting of smaller subsystems 'connected' via a tunable coupling is a challenging task relevant for a variety of physical settings. A general question is whether new phases, not present in the…
We study the two-point correlation functions and the bipartite entanglement in the ground state of the exactly-solvable variable-range extended Ising model of qubits in the presence of a transverse field on a one-dimensional lattice. We…
In this note we overview recent convergence results for correlations in the critical planar nearest-neighbor Ising model. We start with a short discussion of the combinatorics of the model and a definition of fermionic and spinor…