Related papers: Correlated cluster mean-field theory for spin syst…
We derive the exact actions of the $Q$-state Potts model valid on any graph, first for the spin degrees of freedom, and second for the Fortuin-Kasteleyn clusters. In both cases the field is a traceless $Q$-component scalar field…
Classical spin systems with nonadditive long-range interactions are studied in the microcanonical ensemble. It is expected that the entropy of such a system is identical to that of the corresponding mean-field model, which is called…
A novel mean-field approximation for quasi-one-dimensional (Q1D) quantum magnets is formulated. Our new mean-field approach is based on the Bethe-type effective-field theory, where thermal and quantum fluctuations between the…
The ground state and thermodynamics of a generalized spin-1/2 Ising-Heisenberg diamond chain with the second-neighbor interaction between nodal spins are calculated exactly using the mapping method based on the decoration-iteration…
Motivated by a recent proposal of a Bethe approximation for the triangular Ising antiferromagnet [Phys. Rev. B {\bf 56}, 8241 (1997)], which seems to predict a disordered phase at any temperature in zero field, we analyze in some detail…
We apply the coupled cluster method (CCM) to the Hamiltonian version of the latticised O(4) non-linear sigma model. The method, which was initially developed for the accurate description of quantum many-body systems, gives rise to two…
Clustered solutions in oscillator networks provide an important insight into how a system might diversify from a synchronous solution into spatiotemporal complex solutions. They can therefore form a link between fully synchronized and…
The fact that mean field theory is appropriate to describe an Ising model with long-range interactions has been already shown by Cannas and Tamarit. Although not explicited in our Letter, we have used periodic boundary conditions in all our…
Ising model with quenched random magnetic fields is examined for single Gaussian, bimodal and double Gaussian random field distributions by introducing an effective field approximation that takes into account the correlations between…
A procedure to predict the occurrence of periodic clusters in a system of globally coupled maps displaying a constant mean field is presented. The method employs the analogy between a system of globally coupled maps and a single map driven…
For theoretical description of pseudospin systems with essential short-range and long-range interactions we use the method based on calculations of the free energy functional with taking into account the short-range interactions within the…
There is growing empirical evidence that spherical $k$-means clustering performs well at identifying groups of concomitant extremes in high dimensions, thereby leading to sparse models. We provide one of the first theoretical results…
We analyze the structure of fluctuations near critical points and spinodals in mean-field and near-mean-field systems. Unlike systems that are non-mean-field, for which a fluctuation can be represented by a single cluster in a properly…
Finding the ground state of Ising spin glasses is notoriously difficult due to disorder and frustration. Often, this challenge is framed as a combinatorial optimization problem, for which a common strategy employs simulated annealing, a…
This paper establishes a CLT for linear statistics of the form $\langle \mathbf{q},\boldsymbol{\sigma} \rangle$ with quantitative Berry-Esseen bounds, where $\boldsymbol{\sigma}$ is an observation from an exponential family with a quadratic…
An efficient O(N) cluster Monte Carlo method for Ising models with long-range interactions is presented. Our novel algorithm does not introduce any cutoff for interaction range and thus it strictly fulfills the detailed balance. The…
We use numerical linked cluster expansions to study thermodynamic properties of the two-dimensional spin-1/2 Ising, XY, and Heisenberg models with bimodal random-bond disorder on the square and honeycomb lattices. In all cases, the…
It is shown that a spin system is equivalent to a set of constrained harmonic oscillators. For finite, but large, systems, a continuous approximation to the density of states can be used, and the oscillator frequencies can be exactly…
Clustering provides a common means of identifying structure in complex data, and there is renewed interest in clustering as a tool for the analysis of large data sets in many fields. A natural question is how many clusters are appropriate…
The extended dynamical mean field theory has played an important role in the study of quantum phase transitions in heavy fermion systems. In order to incorporate the physics of unconventional superconductivity, we develop a cluster version…