158 research outputs found
Berezinians, Exterior Powers and Recurrent Sequences
We study power expansions of the characteristic function of a linear operator
in a -dimensional superspace . We show that traces of exterior
powers of satisfy universal recurrence relations of period .
`Underlying' recurrence relations hold in the Grothendieck ring of
representations of \GL(V). They are expressed by vanishing of certain Hankel
determinants of order in this ring, which generalizes the vanishing of
sufficiently high exterior powers of an ordinary vector space. In particular,
this allows to explicitly express the Berezinian of an operator as a rational
function of traces. We analyze the Cayley--Hamilton identity in a superspace.
Using the geometric meaning of the Berezinian we also give a simple formulation
of the analog of Cramer's rule.Comment: 35 pages. LaTeX 2e. New version: paper substantially reworked and
expanded, new results include
Phase Diagram of the BCC S=1/2 Heisenberg Antiferromagnet with First and Second Neighbor Exchange
We use linked-cluster series expansions, both at T=0 and high temperature, to
analyse the phase structure of the spin-\half Heisenberg antiferromagnet with
competing first and second-neighbor interactions on the 3-dimensional
body-centred-cubic lattice. At zero temperature we find a first-order quantum
phase transition at between AF (Ne\'el)
and AF ordered phases. The high temperature series yield quite accurate
estimates of the bounding critical line for the AF phase, and an apparent
critical line for the AF phase, with a bicritical point at , . The possibility that this latter transition is
first-order cannot be excluded.Comment: 10 pages, 4 figure
Series study of the One-dimensional S-T Spin-Orbital Model
We use perturbative series expansions about a staggered dimerized ground
state to compute the ground state energy, triplet excitation spectra and
spectral weight for a one-dimensional model in which each site has an S=\case
1/2 spin and a pseudospin , representing a doubly
degenerate orbital. An explicit dimerization is introduced to allow study of
the confinement of spinon excitations. The elementary triplet represents a
bound state of two spinons, and is stable over much of the Brillouine zone. A
special line is found in the gapped spin-liquid phase, on which the triplet
excitation is dispersionless. The formation of triplet bound states is also
investigated.Comment: 9 pages, 9 figure
Quantum disorder in the two-dimensional pyrochlore Heisenberg antiferromagnet
We present the results of an exact diagonalization study of the spin-1/2
Heisenberg antiferromagnet on a two-dimensional version of the pyrochlore
lattice, also known as the square lattice with crossings or the checkerboard
lattice. Examining the low energy spectra for systems of up to 24 spins, we
find that all clusters studied have non-degenerate ground states with total
spin zero, and big energy gaps to states with higher total spin. We also find a
large number of non-magnetic excitations at energies within this spin gap.
Spin-spin and spin-Peierls correlation functions appear to be short-ranged, and
we suggest that the ground state is a spin liquid.Comment: 7 pages, 11 figures, RevTeX minor changes made, Figure 6 correcte
Generalized Drinfeld-Sokolov Reductions and KdV Type Hierarchies
Generalized Drinfeld-Sokolov (DS) hierarchies are constructed through local
reductions of Hamiltonian flows generated by monodromy invariants on the dual
of a loop algebra. Following earlier work of De Groot et al, reductions based
upon graded regular elements of arbitrary Heisenberg subalgebras are
considered. We show that, in the case of the nontwisted loop algebra
, graded regular elements exist only in those Heisenberg
subalgebras which correspond either to the partitions of into the sum of
equal numbers or to equal numbers plus one . We prove that the
reduction belonging to the grade regular elements in the case yields
the matrix version of the Gelfand-Dickey -KdV hierarchy,
generalizing the scalar case considered by DS. The methods of DS are
utilized throughout the analysis, but formulating the reduction entirely within
the Hamiltonian framework provided by the classical r-matrix approach leads to
some simplifications even for .Comment: 43 page
Renormalization Group Approach to the Coulomb Pseudopotential for C_{60}
A numerical renormalization group technique recently developed by one of us
is used to analyse the Coulomb pseudopotential () in
for a variety of bare potentials. We find a large reduction in due to
intraball screening alone, leading to an interesting non-monotonic dependence
of on the bare interaction strength.
We find that is positive for physically reasonable bare parameters,
but small enough to make the electron-phonon coupling a viable mechanism for
superconductivity in alkali-doped fullerides. We end with some open problems.Comment: 12 pages, latex, 7 figures available from [email protected]
Concern with COVID-19 Pandemic Threat and Attitudes Towards Immigrants:The Mediating Effect of the Desire for Tightness
Tightening social norms is thought to be adaptive for dealing with collective threat yet it may have negative consequences for increasing prejudice. The present research investigated the role of desire for cultural tightness, triggered by the COVID-19 pandemic, in increasing negative attitudes towards immigrants. We used participant-level data from 41 countries (N = 55,015) collected as part of the PsyCorona project, a cross-national longitudinal study on responses to COVID-19. Our predictions were tested through multilevel and SEM models, treating participants as nested within countries. Results showed that people's concern with COVID-19 threat was related to greater desire for tightness which, in turn, was linked to more negative attitudes towards immigrants. These findings were followed up with a longitudinal model (N = 2,349) which also showed that people's heightened concern with COVID-19 in an earlier stage of the pandemic was associated with an increase in their desire for tightness and negative attitudes towards immigrants later in time. Our findings offer insight into the trade-offs that tightening social norms under collective threat has for human groups
Ecological and cultural factors underlying the global distribution of prejudice
Prejudiced attitudes and political nationalism vary widely around the world, but there has
been little research on what predicts this variation. Here we examine the ecological and cultural factors underlying the worldwide distribution of prejudice. We suggest that cultures
grow more prejudiced when they tighten cultural norms in response to destabilizing ecological threats. A set of seven archival analyses, surveys, and experiments (∑N = 3,986,402)
find that nations, American states, and pre-industrial societies with tighter cultural norms
show the most prejudice based on skin color, religion, nationality, and sexuality, and that
tightness predicts why prejudice is often highest in areas of the world with histories of ecological threat. People’s support for cultural tightness also mediates the link between perceived ecological threat and intentions to vote for nationalist politicians. Results replicate
when controlling for economic development, inequality, conservatism, residential mobility,
and shared cultural heritage. These findings offer a cultural evolutionary perspective on prejudice, with implications for immigration, intercultural conflict, and radicalization.publishedVersio
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