Related papers: Generalized Number Theoretic Spin Chain-Connection…
Supersymmetry can be consistently generalized in one and two dimensional spaces, fractional supersymmetry being one of the possible extension. 2D fractional supersymmetry of arbitrary order $F$ is explicitly constructed using an adapted…
We argue that complex systems must possess long range correlations and illustrate this idea on the example of the mean field spin glass model. Defined on the complete graph, this model has no genuine concept of distance, but the long range…
We consider the Farey fraction spin chain in an external field $h$. Using ideas from dynamical systems and functional analysis, we show that the free energy $f$ in the vicinity of the second-order phase transition is given, exactly, by $$ f…
Action-angle type variables for spin generalizations of the elliptic Ruijsenaars-Schneider system are constructed. The equations of motion of these systems are solved in terms of Riemann theta-functions. It is proved that these systems are…
We study the dynamical properties of the random transverse-field Ising chain at criticality using a mapping to free fermions, with which we can obtain numerically exact results for system sizes, L, as large as 256. The probability…
We derive a new representation for spin-spin correlation functions of the finite XXZ spin-1/2 Heisenberg chain in terms of a single multiple integral, that we call the master equation. Evaluation of this master equation gives rise on the…
We will see that key concepts of number theory can be defined for arbitrary operations. We give a generalized distributivity for hyperoperations (usual arithmetic operations and operations going beyond exponentiation) and a generalization…
Baxter's $T-Q$ relation for the periodic spin-$\frac12$ XYZ chain is studied. We extensively perform numerical calculations for the $T-Q$ relation and the Bethe ansatz equations. Numerical based hypotheses are then proposed to answer some…
In this paper, we consider the quantum XYZ open spin-1/2 chain with boundary fields. We focus on the particular case in which the six boundary parameters are related by a single constraint enabling us to describe part of the spectrum by…
Linear finite dynamical systems play an important role, for example, in coding theory and simulations. Methods for analyzing such systems are often restricted to cases in which the system is defined over a field %and usually strive to…
S=1/2 quantum spin chains and ladders with random exchange coupling are studied by using an effective low-energy field theory and transfer matrix methods. Effects of the nonlocal correlations of exchange couplings are investigated…
Certain approximations for the spin expectations have been studied both numerically and theoretically. Approximations are constructed using solutions of the lattice heat equation. The most interesting idea is a certain randomness assumption…
We introduce a fractional generalization of the Erlang Queues $M/E_k/1$. Such process is obtained through a time-change via inverse stable subordinator of the classical queue process. We first exploit the (fractional) Kolmogorov forward…
We discuss certain quadratic models of spinless fermions on a 1D lattice, and their corresponding spin chains. These were studied by Keating and Mezzadri in the context of their relation to the Haar measures of the classical compact groups.…
Systems of integral equations are proposed which generalise those previously encountered in connection with the so-called staircase models. Under the assumption that these equations describe the finite-size effects of relativistic field…
A comprehensive approach to the theory of higher spin gauge fields is proposed. By explicitly separating out details of implementation from general principles, it becomes possible to focus on the bare minimum of requirements that such a…
We propose a new framework for the nested algebraic Bethe ansatz for a closed, rational spin chain with $\mathfrak{g}$-symmetry for any simple Lie algebra $\mathfrak{g}$. Starting the nesting process by removing a single simple root from…
We compute the entropy of entanglement in the ground states of a general class of quantum spin-chain Hamiltonians - those that are related to quadratic forms of Fermi operators - between the first N spins and the rest of the system in the…
We consider the calculation of ground-state expectation values for the non-Hermitian Z(N) spin chain described by free parafermions. For N=2 the model reduces to the quantum Ising chain in a transverse field with open boundary conditions.…
Evolution of the z-component of a single spin in the finite cyclic XY spin 1/2 chain is studied. Initially one selected spin is polarized while other spins are completely unpolarized and uncorrelated. Polarization of the selected spin as a…