12,862 research outputs found
General scalar products in the arbitrary six-vertex model
In this work we use the algebraic Bethe ansatz to derive the general scalar
product in the six-vertex model for generic Boltzmann weights. We performed
this calculation using only the unitarity property, the Yang-Baxter algebra and
the Yang-Baxter equation. We have derived a recurrence relation for the scalar
product. The solution of this relation was written in terms of the domain wall
partition functions. By its turn, these partition functions were also obtained
for generic Boltzmann weights, which provided us with an explicit expression
for the general scalar product.Comment: 24 page
Gaudin Hypothesis for the XYZ Spin Chain
The XYZ spin chain is considered in the framework of the generalized
algebraic Bethe ansatz developed by Takhtajan and Faddeev. The sum of norms of
the Bethe vectors is computed and expressed in the form of a Jacobian. This
result corresponds to the Gaudin hypothesis for the XYZ spin chain.Comment: 12 pages, LaTeX2e (+ amssymb, amsthm); to appear in J. Phys.
Bethe Equations "on the Wrong Side of Equator"
We analyse the famous Baxter's equations for () spin chain
and show that apart from its usual polynomial (trigonometric) solution, which
provides the solution of Bethe-Ansatz equations, there exists also the second
solution which should corresponds to Bethe-Ansatz beyond . This second
solution of Baxter's equation plays essential role and together with the first
one gives rise to all fusion relations.Comment: 13 pages, original paper was spoiled during transmissio
Choosing the Best Online Platform
Social media is a powerful tool that enables forage-livestock researchers and Extension specialists to connect with a wide audience of producers, Extension personnel, colleagues, and industry partners. This presentation in the thematic session on “Understanding the role of social media and digital resources in forage education and promotion” will provide an overview of popular social media platforms (Facebook, Twitter, Instagram, TikTok, and YouTube) and discuss how to transform impactful research and Extension programming into effective social content before leading into the panel discussion
Spin operator matrix elements in the superintegrable chiral Potts quantum chain
We derive spin operator matrix elements between general eigenstates of the
superintegrable Z_N-symmetric chiral Potts quantum chain of finite length. Our
starting point is the extended Onsager algebra recently proposed by R.Baxter.
For each pair of spaces (Onsager sectors) of the irreducible representations of
the Onsager algebra, we calculate the spin matrix elements between the
eigenstates of the Hamiltonian of the quantum chain in factorized form, up to
an overall scalar factor. This factor is known for the ground state Onsager
sectors. For the matrix elements between the ground states of these sectors we
perform the thermodynamic limit and obtain the formula for the order
parameters. For the Ising quantum chain in a transverse field (N=2 case) the
factorized form for the matrix elements coincides with the corresponding
expressions obtained recently by the Separation of Variables Method.Comment: 24 pages, 1 figur
Ising Model on Edge-Dual of Random Networks
We consider Ising model on edge-dual of uncorrelated random networks with
arbitrary degree distribution. These networks have a finite clustering in the
thermodynamic limit. High and low temperature expansions of Ising model on the
edge-dual of random networks are derived. A detailed comparison of the critical
behavior of Ising model on scale free random networks and their edge-dual is
presented.Comment: 23 pages, 4 figures, 1 tabl
Fork rotation and DNA precatenation are restricted during DNA replication to prevent chromosomal instability
Faithful genome duplication and inheritance require the complete resolution of all intertwines within the parental DNA duplex. This is achieved by topoisomerase action ahead of the replication fork or by fork rotation and subsequent resolution of the DNA precatenation formed. Although fork rotation predominates at replication termination, in vitro studies have suggested that it also occurs frequently during elongation. However, the factors that influence fork rotation and how rotation and precatenation may influence other replication-associated processes are unknown. Here we analyze the causes and consequences of fork rotation in budding yeast. We find that fork rotation and precatenation preferentially occur in contexts that inhibit topoisomerase action ahead of the fork, including stable protein–DNA fragile sites and termination. However, generally, fork rotation and precatenation are actively inhibited by Timeless/Tof1 and Tipin/Csm3. In the absence of Tof1/Timeless, excessive fork rotation and precatenation cause extensive DNA damage following DNA replication. With Tof1, damage related to precatenation is focused on the fragile protein–DNA sites where fork rotation is induced. We conclude that although fork rotation and precatenation facilitate unwinding in hard-to-replicate contexts, they intrinsically disrupt normal chromosome duplication and are therefore restricted by Timeless/Tipin
A Generalized Q-operator for U_q(\hat(sl_2)) Vertex Models
In this paper, we construct a Q-operator as a trace of a representation of
the universal R-matrix of over an infinite-dimensional
auxiliary space. This auxiliary space is a four-parameter generalization of the
q-oscillator representations used previously. We derive generalized T-Q
relations in which 3 of these parameters shift. After a suitable restriction of
parameters, we give an explicit expression for the Q-operator of the 6-vertex
model and show the connection with Baxter's expression for the central block of
his corresponding operator.Comment: 22 pages, Latex2e. This replacement is a revised version that
includes a simple explicit expression for the Q matrix for the 6-vertex mode
Analyticity and Integrabiity in the Chiral Potts Model
We study the perturbation theory for the general non-integrable chiral Potts
model depending on two chiral angles and a strength parameter and show how the
analyticity of the ground state energy and correlation functions dramatically
increases when the angles and the strength parameter satisfy the integrability
condition. We further specialize to the superintegrable case and verify that a
sum rule is obeyed.Comment: 31 pages in harvmac including 9 tables, several misprints eliminate
Spiral order by disorder and lattice nematic order in a frustrated Heisenberg antiferromagnet on the honeycomb lattice
Motivated by recent experiments on BiMnO(NO), we study a
frustrated - Heisenberg model on the two dimensional (2D) honeycomb
lattice. The classical - Heisenberg model on the two dimensional (2D)
honeycomb lattice has N\'eel order for , it
exhibits a one-parameter family of degenerate incommensurate spin spiral ground
states where the spiral wave vector can point in any direction. Spin wave
fluctuations at leading order lift this accidental degeneracy in favor of
specific wave vectors, leading to spiral order by disorder. For spin ,
quantum fluctuations are, however, likely to be strong enough to melt the
spiral order parameter over a wide range of . Over a part of this
range, we argue that the resulting state is a valence bond solid (VBS) with
staggered dimer order - this VBS is a nematic which breaks lattice rotational
symmetry. Our arguments are supported by comparing the spin wave energy with
the energy of the dimer solid obtained using a bond operator formalism. Turning
to the effect of thermal fluctuations on the spiral ordered state, any nonzero
temperature destroys the magnetic order, but the discrete rotational symmetry
of the lattice remains broken resulting in a thermal analogue of the nematic
VBS. We present arguments, supported by classical Monte Carlo simulations, that
this nematic transforms into the high temperature symmetric paramagnet via a
thermal phase transition which is in the universality class of the classical
3-state Potts (clock) model in 2D. We discuss the possible relevance of our
results for honeycomb magnets, such as BiMO(NO) (with
M=Mn,V,Cr), and bilayer triangular lattice magnets.Comment: Slightly revise
- …