Related papers: Four-Weight Spin Models and Jones Pairs
Spinons are among the generic excitations in one-dimensional spin systems, they can be massless or massive. The quantitative description of massive spinons poses a considerable challenge in spite of various variational approaches. We show…
The notion of multivariate $P$- and $Q$-polynomial association scheme has been introduced recently, generalizing the well-known univariate case. Numerous examples of such association schemes have already been exhibited. In particular, it…
The Wegner $Z_2$ gauge theory-$Z_2$ Ising spin model duality in $(2+1)$ dimensions is revisited and derived through a series of canonical transformations. The Kramers-Wannier duality is similarly obtained. The Wegner $Z_2$ gauge-spin…
We propose a scheme for constructing classical spin Hamiltonians from Hunds coupled spin-fermion models in the limit J_H/t \to \infinity. The strong coupling between fermions and the core spins requires self-consistent calculation of the…
We introduce a generalization of the Stirling numbers via symmetric functions involving two weight functions. The resulting extension unifies previously known Stirling-type sequences with known symmetric function forms, as well as other…
This brief review surveys recent progress driven by the gauge/Yang-Baxter equation (YBE) correspondence. This connection has proven to be a powerful tool for discovering novel integrable lattice spin models in statistical mechanics by…
It can be conjectured that the colored Jones function of a knot can be computed in terms of counting paths on the graph of a planar projection of a knot. On the combinatorial level, the colored Jones function can be replaced by its weight…
The distinct models that describe spin 1 and 2 massive excitations in 2+1 dimensions are analized, showing their equivalence (between models of same spin) and analogies (between models of different spin). Topics as spontaneous symmetry…
We present an alternative formalism for modeling spin. The ontological elements of this formalism are base-2 sequences of length $n$. The machinery necessary to model physics is then developed by considering correlations between base-2…
An open question akin to the slice-ribbon conjecture asks whether every ribbon knot can be represented as a symmetric union. Next to this basic existence question sits the question of uniqueness of such representations. Eisermann and Lamm…
Pair correlations are described in the framework of the HFB approximation applied to a uniformly rotating system (Cranking model). The reduction of the moments of inertia, the classification of rotational bands as multi quasiparticle…
We use the methods of group theory to reduce the equations of motion of two spin systems in (2+1) dimensions to sets of coupled ordinary differential equations. We present solutions of some classes of these sets and discuss their physical…
In this paper, we classify all spin models for singly-generated Yang-Baxter planar algebras in terms of certain highly regular graphs. Using Liu's classification of singly generated Yang-Baxter planar algebras, this classifies all spin…
We explain the use of dual quaternions to represent poses, twists, and wrenches.
We give a brief overview of some three-dimensional toy models for higher-spin interactions. We first review the construction of pure higher-spin gauge theories in terms of Chern-Simons theories. We then discuss how this setup could be…
We present a construction of the reaction amplitude for the inclusive production of a resonance decaying to a pair of identical vector particles such as $J/\psi J/\psi$, $\rho\rho$, $\phi\phi$. The method provides the possibility of…
Using complexified quaternions, an intriguing link between generators of two different and surprisingly commuting four-dimensional representations of the SU(2)xU(1) Lie group, and generators of two four-dimensional spin 1/2 representations…
We study the issue of coupling among 4-simplices in the context of spin foam models obtained from a group field theory formalism. We construct a generalisation of the Barrett-Crane model in which an additional coupling between the normals…
Based on the Majumdar-Ghosh chain we construct several spin models which allow us to investigate spinon dynamics in the regime close to deconfinement of spinons. We consider the J_1 - J_2 - \delta model, two coupled J_1 - J_2 chains…
A key step in unraveling the mysteries of materials exhibiting unconventional superconductivity is to understand the underlying pairing mechanism. While it is widely agreed upon that the pairing glue in many of these systems originates from…