Berezinians, Exterior Powers and Recurrent Sequences

We study power expansions of the characteristic function of a linear operator $A$ in a $p|q$-dimensional superspace $V$. We show that traces of exterior powers of $A$ satisfy universal recurrence relations of period $q$. `Underlying' recurrence relations hold in the Grothendieck ring of representations of \GL(V). They are expressed by vanishing of certain Hankel determinants of order $q+1$ 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 $J_2/J_1 \simeq 0.705 \pm 0.005$ between AF$_1$ (Ne\'el) and AF$_2$ ordered phases. The high temperature series yield quite accurate estimates of the bounding critical line for the AF$_1$ phase, and an apparent critical line for the AF$_2$ phase, with a bicritical point at $J_1/J_2\simeq 0.71$, $kT/J_1\simeq 0.34$. 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 ${\bf S}_i$ and a pseudospin ${\bf T}_i$, 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 $\ell(gl_n)$, graded regular elements exist only in those Heisenberg subalgebras which correspond either to the partitions of $n$ into the sum of equal numbers $n=pr$ or to equal numbers plus one $n=pr+1$. We prove that the reduction belonging to the grade $1$ regular elements in the case $n=pr$ yields the $p\times p$ matrix version of the Gelfand-Dickey $r$-KdV hierarchy, generalizing the scalar case $p=1$ 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 $p=1$.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 (${\mu^*}$) in ${{\rm C}_{60}}$ for a variety of bare potentials. We find a large reduction in ${\mu^*}$ due to intraball screening alone, leading to an interesting non-monotonic dependence of ${\mu^*}$ on the bare interaction strength. We find that ${\mu^*}$ 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