Related papers: Azbel-Hofstadter model on triangular lattice revis…
Lyapunov exponents describe the asymptotic behavior of the singular values of large products of random matrices. A direct computation of these exponents is however often infeasible. By establishing a link between Lyapunov exponents and an…
Lyapunov exponents are well-known characteristic numbers that describe growth rates of perturbations applied to a trajectory of a dynamical system in different state space directions. Covariant (or characteristic) Lyapunov vectors indicate…
We develop series expansions for the ground state properties of the Hubbard model, by introducing an Ising anisotropy into the Hamiltonian. For the two-dimensional (2D) square lattice half-filled Hubbard model, the ground state energy,…
In a previous paper (arXiv:2510.19746), we have studied the maximal hard-code model on the square lattice ${\mathbb Z}^2$ from the perspective of recoverable systems. Here we extend this study to the case of the triangular lattice ${\mathbb…
This paper treats iterative solution methods to the generalized Lyapunov equation. Specifically it expands the existing theoretical justification for the alternating linear scheme (ALS) from the stable Lyapunov equation to the stable…
Nonparametric density and regression estimators commonly depend on a bandwidth. The asymptotic properties of these estimators have been widely studied when bandwidths are nonstochastic. In practice, however, in order to improve finite…
The Ising approximation of the Heisenberg model in a strong magnetic field, with two, three and six spin exchange interactions is studied on a kagome chain. The kagome chain can be considered as an approximation of the third layer of 3He…
The article is devoted to the geometry of solutions to the chordal Loewner equation which is based on the comparison of singular solutions and harmonic measures for the sides of a slit in the upper half-plane generated by a driving term. An…
Through applying Bell polynomials to the integral representation of the free energy of the Ising model for the triangular and hexagonal lattices we obtain the exact combinatorial formulas for the number of spin configurations at a given…
The dynamics of a system consisting of many spherical hard particles can be described as a single point particle moving in a high-dimensional space with fixed hypercylindrical scatterers with specific orientations and positions. In this…
We consider Boltzmann random triangulations coupled to the Ising model on their faces, under Dobrushin boundary conditions and at the critical point of the model. The first part of this paper computes explicitly the partition function of…
A harmonic triangular lattice with a vacancy under imposed volumetric strain is considered. Simple asymptotic formula for the displacement field is derived. The formula has reasonable accuracy at all lattice nodes. Strain concentration…
We use numerical transfer-matrix methods to investigate properties of the multicriticalpoint of binary Ising spin glasses on a square lattice, whose location we assume to be given exactly by a conjecture advanced by Nishimori and Nemoto. We…
We describe a general expansion of spherical (full-sky) bispectra into a set of orthogonal modes. For squeezed shapes, the basis separates physically-distinct signals and is dominated by the lowest moments. In terms of reduced bispectra, we…
We consider generalized linear stochastic dynamical systems with second-order state transition matrices. The entries of the matrix are assumed to be either independent and exponentially distributed or equal to zero. We give an overview of…
Lyapunov exponents can be difficult to determine from experimental data. In particular, when using embedding theory to build chaotic attractors in a reconstruction space, extra "spurious" Lyapunov exponents arise that are not Lyapunov…
There is no an accepted exact partition function (PF) for the three dimensional (3D) Ising model to our knowledge. Mainly based on the connection between the lattice Green function (LGF) for the simple cubic lattice and that for the…
The problem of finding of the ferromagnetic and antiferromagnetic "symmetry broken" solutions of the correlated lattice fermion models beyond the mean-field approximation has been investigated. The calculation of the quasiparticle…
A method is proposed for exactly calculating the partition function of a rectangular Ising lattice with the presence of a uniform external field. This approach is based on the method of the transfer matrix developed about seventy years ago…
We study integrability breaking and transport in a discrete space-time lattice with a local integrability breaking perturbation. We find a singular distribution of the Lyapunov spectrum where the majority of Lyapunov exponents vanish in the…