Related papers: Spin systems with hyperbolic symmetry: a survey
A simple and transparent example of a non-autonomous flow system, with hyperbolic strange attractor is suggested. The system is constructed on a basis of two coupled van der Pol oscillators, the characteristic frequencies differ twice, and…
Spherically symmetric random walks in arbitrary dimension $D$ can be described in terms of Gegenbauer (ultraspherical) polynomials. For example, Legendre polynomials can be used to represent the special case of two-dimensional spherically…
We investigate the non-Hermitian (NH) attractive Hubbard model with spin depairing, which is a spin-resolved asymmetric hopping that nonreciprocally operates spins in the opposite direction. We find that spin depairing stabilizes a…
The phenomenon of Anderson localization wherein non-interacting electrons are localized by quenched impurities is a subject matter that has been extremely well studied. However, localization transition under the combined influence of…
Theoretical study is performed of a single-mode polariton system with linear coupling of spin components. When combined with an ordinary two-particle interaction, the spin coupling involves a spontaneous symmetry breaking accompanied by a…
We investigate certain classes of integrable classical or quantum spin systems. The first class is characterized by the recursively defined property $P$ saying that the spin system consists of a single spin or can be decomposed into two…
We show that a simple two dimensional model of spin crossover materials gives rise to spin-state smectic phases where the pattern of high-spin (HS) and low-spin (LS) metal centers spontaneously breaks rotational symmetry and translational…
The self-avoiding walk, and lattice spin systems such as the $\varphi^4$ model, are models of interest both in mathematics and in physics. Many of their important mathematical problems remain unsolved, particularly those involving critical…
In this Perspective article, we explore some of the promising spin and topology material platforms (e.g. spins in semi- and superconductors, skyrmionic, topological and 2D materials) being developed for such quantum components as qubits,…
In this paper, we present the possibility of using the Ising like models to explain by Statistical Physics means the connection between the financial discontinuities (herd behavior, bubbles, crashes) and "critical points" in physical of…
We discuss a simple procedure for obtaining new integrable spin chains from old by replacing each single state of the original model by some collection of states. This works whenever the Lax matrix of the chain has a certain form. The…
The typicality approach and the Hilbert space averaging method as its technical manifestation are important concepts of quantum statistical mechanics. Extensively used for expectation values we extend them in this paper to transition…
The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…
The models surveyed include generalized P\'{o}lya urns, reinforced random walks, interacting urn models, and continuous reinforced processes. Emphasis is on methods and results, with sketches provided of some proofs. Applications are…
This work is concerned with relaxation models arising from numerical schemes for hyperbolic-parabolic systems. Such models are a hyperbolic system with both the hyperbolic part and the stiff source term involving a small positive parameter,…
In classical spin systems with two largely different inherent time scales, the configuration of the fast spins almost instantaneously follows the slow-spin dynamics. We develop the emergent effective theory for the slow-spin degrees of…
Studies of disordered spin chains have recently experienced a renewed interest, inspired by the question to which extent the exact numerical calculations comply with the existence of a many-body localization phase transition. For the…
The two-dimensional hyperbolic plane, $\mathbb{H}^2$, is an unusual system in that dimensionality changes with scale: locally two-dimensional and planar at short distances, but effectively infinite-dimensional at large scales, it provides…
Chirality-induced spin selectivity is a spin-splitting phenomenon from a helical structure with a considerably effective spin-orbit coupling. This unexpectedly large spin-splitting phenomenon has been experimentally observed in chiral…
We study Ising spin models on finitely connected random interaction graphs which are drawn from an ensemble in which not only the degree distribution $p(k)$ can be chosen arbitrarily, but which allows for further fine-tuning of the topology…