Phase Diagram of the 1D Kondo Lattice Model

We determine the boundary of the fully polarized ferromagnetic ground state in the one dimensional Kondo lattice model at partial conduction electron band filling by using a newly developed infinite size DMRG method which conserves the total spin quantum number. The obtained paramagnetic to ferromagnetic phase boundary is below $J \approx 3.5$ for the whole range of band filling. By this we solve the controversy in the phase diagram over the extent of the ferromagnetic region close to half filling.Comment: 6 pages, 4 EPS figures. Presented at MOS9

Isotope effect on superconductivity in Josephson coupled stripes in underdoped cuprates

Inelastic neutron scattering data for YBaCuO as well as for LaSrCuO indicate incommensurate neutron scattering peaks with incommensuration $\delta(x)$ away from the $(\pi,\pi)$ point. $T_c(x)$ can be replotted as a linear function of the incommensuration for these materials. This linear relation implies that the constant that relates these two quantities, one being the incommensuration (momentum) and another being $T_c(x)$ (energy), has the dimension of velocity we denote $v^*$: $k_B T_c(x) = \hbar v^* \delta(x)$. We argue that this experimentally derived relation can be obtained in a simple model of Josephson coupled stripes. Within this framework we address the role of the $O^{16} \to O^{18}$ isotope effect on the $T_c(x)$. We assume that the incommensuration is set by the {\em doping} of the sample and is not sensitive to the oxygen isotope given the fixed doping. We find therefore that the only parameter that can change with O isotope substitution in the relation $T_c(x) \sim \delta(x)$ is the velocity $v^*$. We predict an oxygen isotope effect on $v^*$ and expect it to be $\simeq 5$.Comment: 4 pages latex file, 2 eps fig

Universal Amplitude Ratios in the Ising Model in Three Dimensions

We use a high-precision Monte Carlo simulation to determine the universal specific-heat amplitude ratio A+/A- in the three-dimensional Ising model via the impact angle \phi of complex temperature zeros. We also measure the correlation-length critical exponent \nu from finite-size scaling, and the specific-heat exponent \alpha through hyperscaling. Extrapolations to the thermodynamic limit yield \phi = 59.2(1.0) degrees, A+/A- = 0.56(3), \nu = 0.63048(32) and \alpha = 0.1086(10). These results are compatible with some previous estimates from a variety of sources and rule out recently conjectured exact values.Comment: 17 pages, 5 figure

Spinful bosons in an optical lattice

We analyze the behavior of cold spin-1 particles with antiferromagnetic interactions in a one-dimensional optical lattice using density matrix renormalization group calculations. Correlation functions and the dimerization are shown and we also present results for the energy gap between ground state and the spin excited states. We confirm the anticipated phase diagram, with Mott-insulating regions of alternating dimerized S=1 chains for odd particle density versus on-site singlets for even density. We find no evidence for any additional ordered phases in the physically accessible region, however for sufficiently large spin interaction, on-site singlet pairs dominate leading, for odd density, to a breakdown of the Mott insulator or, for even density, a real-space singlet superfluid.Comment: Minor revisions and clarification

On the p,qp,q-binomial distribution and the Ising model

A completely new approach to the Ising model in 1 to 5 dimensions is developed. We employ $p,q$-binomial coefficients, a generalisation of the binomial coefficients, to describe the magnetisation distributions of the Ising model. For the complete graph this distribution corresponds exactly to the limit case $p=q$. We take our investigation to the simple $d$-dimensional lattices for $d=1,2,3,4,5$ and fit $p,q$-binomial distributions to our data, some of which are exact but most are sampled. For $d=1$ and $d=5$ the magnetisation distributions are remarkably well-fitted by $p,q$-binomial distributions. For $d=4$ we are only slightly less successful, while for $d=2,3$ we see some deviations (with exceptions!) between the $p,q$-binomial and the Ising distribution. We begin the paper by giving results on the behaviour of the $p,q$-distribution and its moment growth exponents given a certain parameterization of $p,q$. Since the moment exponents are known for the Ising model (or at least approximately for $d=3$) we can predict how $p,q$ should behave and compare this to our measured $p,q$. The results speak in favour of the $p,q$-binomial distribution's correctness regarding their general behaviour in comparison to the Ising model. The full extent to which they correctly model the Ising distribution is not settled though.Comment: 51 pages, 23 figures, submitted to PRB on Oct 23 200

SOS model partition function and the elliptic weight functions

We generalize a recent observation [arXiv:math/0610433] that the partition function of the 6-vertex model with domain-wall boundary conditions can be obtained by computing the projections of the product of the total currents in the quantum affine algebra $U_{q}(\hat{\mathfrak{sl}}_{2})$ in its current realization. A generalization is proved for the the elliptic current algebra [arXiv:q-alg/9703018,arXiv:q-alg/9601022]. The projections of the product of total currents are calculated explicitly and are represented as integral transforms of the product of the total currents. We prove that the kernel of this transform is proportional to the partition function of the SOS model with domain-wall boundary conditions.Comment: 21 pages, 5 figures, requires iopart packag

On the low-temperature phase of the three-state antiferromagnetic Potts model on the simple cubic lattice

The three-state antiferromagnetic Potts model on the simple cubic lattice is investigated using the cluster variation method in the cube and the star-cube approximations. The broken-sublattice-symmetry phase is found to be stable in the whole low-temperature region, contrary to previous results obtained using a modified cluster variation method. The tiny free energy difference between the broken-sublattice-symmetry and the permutationally-symmetric-sublattices phases is calculated in the two approximations and turns out to be smaller in the (more accurate) star-cube approximation than in the cube one.Comment: 4 pages REVTeX + 2 PostScript figures, to be published in Phys. Rev. E as a Rapid Communicatio

Essentialist Reasoning and Knowledge Effects on Biological Reasoning in Young Children

Biological kinds undergo a variety of changes during their life span, and these changes vary in degree by organism. Understanding that an organism, such as a caterpillar, maintains category identity over its life span despite dramatic changes is a key concept in biological reasoning. At present, we know little about the developmental trajectory of children’s understanding of dramatic life-cycle changes and how this might relate to their understanding of evolution. We suggest that this understanding is a key precursor to later understanding of evolutionary change. Two studies examined the impact of age and knowledge on children’s biological reasoning about living kinds that undergo a range of natural life-span changes—from subtle to dramatic. The participants, who were 3, 4, and 7 years old, were shown paired pictures of juvenile and adult animals and asked to endorse biological or nonbiological causal mechanisms to account for life-span change. Additionally, reasoning of 3- and 4-year-old participants was compared before and after exposure to caterpillars transforming into butterflies. The results are framed in terms of a developmental trajectory in essentialist reasoning, a cognitive bias that has been associated with difficulties in understanding and accepting evolution