39 research outputs found
Partition functions of Polychronakos like spin chains associated with polarized spin reversal operators
We construct polarized spin reversal operator (PSRO) which yields a class of
representations for the type of Weyl algebra, and subsequently use this
PSRO to find out novel exactly solvable variants of the type of spin
Calogero model. The strong coupling limit of such spin Calogero models
generates the type of Polychronakos spin chains with PSRO. We derive the
exact spectra of the type of spin Calogero models with PSRO and compute
the partition functions of the related spin chains by using the freezing trick.
We also find out an interesting relation between the partition functions of the
type and type of Polychronakos spin chains. Finally, we study
spectral properties like level density and distribution of spacing between
consecutive energy levels for type of Polychronakos spin chains with
PSRO.Comment: 34 pages, 2 figures, minor typos corrected, 3 references adde
One-Dimensional Vertex Models Associated with a Class of Yangian Invariant Haldane-Shastry Like Spin Chains
We define a class of Yangian invariant Haldane-Shastry (HS)
like spin chains, by assuming that their partition functions can be written in
a particular form in terms of the super Schur polynomials. Using some
properties of the super Schur polynomials, we show that the partition functions
of this class of spin chains are equivalent to the partition functions of a
class of one-dimensional vertex models with appropriately defined energy
functions. We also establish a boson-fermion duality relation for the partition
functions of this class of supersymmetric HS like spin chains by using their
correspondence with one-dimensional vertex models
Boson-fermion duality in SU(m|n) supersymmetric Haldane-Shastry spin chain
By using the Y(gl(m|n)) super Yangian symmetry of the SU(m|n) supersymmetric
Haldane-Shastry spin chain, we show that the partition function of this model
satisfies a duality relation under the exchange of bosonic and fermionic spin
degrees of freedom. As a byproduct of this study of the duality relation, we
find a novel combinatorial formula for the super Schur polynomials associated
with some irreducible representations of the Y(gl(m|n)) Yangian algebra.
Finally, we reveal an intimate connection between the global SU(m|n) symmetry
of a spin chain and the boson-fermion duality relation.Comment: 26 pages, no figures; corrected some typo
A CRITICAL REVIEW OF SEGMENTATION
Segmentation as a marketing concept has been viewed as the first step in analysing a market so as to divide the market into component parts consisting of a homogeneous group. Segmentation has evolved from being a simple concept to becoming a major guidance for firms’ strategy and resource allocation. This paper critically reviews the segmentation approaches in a business-to-business context taking into account the differentiated need in a specialized B2B market. The methodology adopted is to review and contrast segmentation literature in traditional and contemporary themes. The review details a critical discussion on business-to-business segmentation with a balanced perspective of a marketing theorist and a strategy practitioner
Exact partition function of SU(m|n) supersymmetric Haldane-Shastry spin chain
By taking the freezing limit of a spin Calogero-Sutherland model containing
`anyon like' representation of the permutation algebra, we derive the exact
partition function of SU(m|n) supersymmetric Haldane-Shastry (HS) spin chain.
This partition function allows us to study global properties of the spectrum
like level density distribution and nearest neighbour spacing distribution. It
is found that, for supersymmetric HS spin chains with large number of lattice
sites, continuous part of the energy level density obeys Gaussian distribution
with a high degree of accuracy. The mean value and standard deviation of such
Gaussian distribution can be calculated exactly. We also conjecture that the
partition function of supersymmetric HS spin chain satisfies a duality relation
under the exchange of bosonic and fermionic spin degrees of freedom.Comment: Latex, 32 pages, 4 figures, minor typos corrected, to be published in
Nucl. Phys.
Low energy properties of the SU(m|n) supersymmetric Haldane-Shastry spin chain
The ground state and low energy excitations of the SU(m|n) supersymmetric
Haldane-Shastry spin chain are analyzed. In the thermodynamic limit, it is
found that the ground state degeneracy is finite only for the SU(m|0) and
SU(m|1) spin chains, while the dispersion relation for the low energy and low
momentum excitations is linear for all values of m and n. We show that the low
energy excitations of the SU(m|1) spin chain are described by a conformal field
theory of m non-interacting Dirac fermions which have only positive energies;
the central charge of this theory is m/2. Finally, for n \ge 1, the partition
functions of the SU(m|n) Haldane-Shastry spin chain and the SU(m|n)
Polychronakos spin chain are shown to be related in a simple way in the
thermodynamic limit at low temperatures.Comment: 40 pages including 2 figures; added some references; this version
will appear in Nuclear Physics
Founder as Steward or Agent? A Study of Founder Ownership and Firm Value
This study addresses the relationship between founder ownership and firm value in young and entrepreneurial businesses. We argue that a stewardship effect prevails when founders have low or high levels of ownership whilst an agency effect prevails at intermediate levels. Using a dataset of 1,269 firms with 11,645 firm–year observations, we find support for our hypothesis that there is a convex relationship between founder ownership and firm value. The agency effect at intermediate founder ownership is consistent with evidence indicating that these firms display lower leverage, greater unrelated diversification, and higher disproportionate board representation