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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…

Mathematical Physics · Physics 2020-12-24 David Sutter , Omar Fawzi , Renato Renner

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…

Chaotic Dynamics · Physics 2012-03-28 Pavel V. Kuptsov , Ulrich Parlitz

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,…

Condensed Matter · Physics 2009-10-28 Zhu-Pei Shi , Rajiv R. P. Singh

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…

Combinatorics · Mathematics 2026-04-16 Geyang Wang , Alexander Barg , Navin Kashyap

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…

Numerical Analysis · Mathematics 2019-06-18 Tobias Breiten , Emil Ringh

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…

Statistics Theory · Mathematics 2014-09-02 Carlos Martins-Filho , Paulo Saraiva

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…

Statistical Mechanics · Physics 2011-02-15 N. Ananikian , L. Ananikyan , R. Artuso , H. Lazaryan

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…

Complex Variables · Mathematics 2014-08-06 Dmitri Prokhorov , Dmitrii Ukrainskii

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…

Mathematical Physics · Physics 2020-08-03 Grzegorz Siudem , Agata Fronczak

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…

Chaotic Dynamics · Physics 2009-11-11 Astrid S. de Wijn

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…

Probability · Mathematics 2021-03-30 Linxiao Chen , Joonas Turunen

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…

Materials Science · Physics 2017-06-08 V. A. Tsaplin , V. A. Kuzkin

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…

Statistical Mechanics · Physics 2007-05-23 Jean C. Lessa , S. L. A. de Queiroz

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…

Cosmology and Nongalactic Astrophysics · Physics 2024-07-23 Julien Carron , Antony Lewis

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…

Optimization and Control · Mathematics 2012-12-27 Nikolai Krivulin

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…

Chaotic Dynamics · Physics 2007-05-23 Joshua A. Tempkin

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…

Statistical Mechanics · Physics 2020-10-26 Rong Qiang Wei

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…

Strongly Correlated Electrons · Physics 2007-05-23 A. L. Kuzemsky

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…

General Physics · Physics 2013-10-02 C. B. Yang

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…

Statistical Mechanics · Physics 2025-09-05 Jiaozi Wang , Tomaž Prosen , Giulio Casati