Anthropic Reasons for Non-Zero Flatness and Lambda

In some cosmological theories with varying constants there are anthropic reasons why the expansion of the universe must not be too {\it close} to flatness or the cosmological constant too close to zero. Using exact theories which incorporate time-variations in $\alpha$ and in $G$ we show how the presence of negative spatial curvature and a positive cosmological constant play an essential role in bringing to an end variations in the scalar fields driving time change in these 'constants' during any dust-dominated era of a universe's expansion. In spatially flat universes with $\Lambda =0$ the fine structure constant grows to a value which makes the existence of atoms impossible.Comment: 7 pages, 5 figures, Corrected sign error and made necessary modifications. This version is accepted for publication in Phys.Rev.

Susceptibility of the 2D S=1/2 Heisenberg antiferromagnet with an impurity

We use a quantum Monte Carlo method (stochastic series expansion) to study the effects of a magnetic or nonmagnetic impurity on the magnetic susceptibility of the two-dimensional Heisenberg antiferromagnet. At low temperatures, we find a log-divergent contribution to the transverse susceptibility. We also introduce an effective few-spin model that can quantitatively capture the differences between magnetic and nonmagnetic impurities at high and intermediate temperatures.Comment: 5 pages, 4 figures, v2: Updated data in figures, minor changes in text, v3: Final version, cosmetic change

Accessing the dynamics of large many-particle systems using Stochastic Series Expansion

The Stochastic Series Expansion method (SSE) is a Quantum Monte Carlo (QMC) technique working directly in the imaginary time continuum and thus avoiding "Trotter discretization" errors. Using a non-local "operator-loop update" it allows treating large quantum mechanical systems of many thousand sites. In this paper we first give a comprehensive review on SSE and present benchmark calculations of SSE's scaling behavior with system size and inverse temperature, and compare it to the loop algorithm, whose scaling is known to be one of the best of all QMC methods. Finally we introduce a new and efficient algorithm to measure Green's functions and thus dynamical properties within SSE.Comment: 11 RevTeX pages including 7 figures and 5 table

NMR relaxation rates for the spin-1/2 Heisenberg chain

The spin-lattice relaxation rate $1/T_1$ and the spin echo decay rate $1/T_{2G}$ for the spin-$1\over 2$ antiferromagnetic Heisenberg chain are calculated using quantum Monte Carlo and maximum entropy analytic continuation. The results are compared with recent analytical calculations by Sachdev. If the nuclear hyperfine form factor $A_q$ is strongly peaked around $q=\pi$ the predicted low-temperature behavior [$1/T_1 \sim \ln{^{1/2}(1/T)}$, $1/T_{2G} \sim \ln{^{1/2}(1/T)}/\sqrt{T}$] extends up to temperatures as high as $T/J \approx 0.5$. If $A_q$ has significant weight for $q \approx 0$ there are large contributions from diffusive long-wavelength processes not taken into account in the theory, and very low temperatures are needed in order to observe the asymptotic $T \to 0$ forms.Comment: 9 pages, Revtex 3.0, 5 uuencoded ps figures To appear in Phys. Rev. B, Rapid Com

Variations of Alpha in Space and Time

We study inhomogeneous cosmological variations in the fine structure 'constant', $\alpha ,$ in Friedmann universes. Inhomogeneous motions of the scalar field driving changes in $\alpha$ display spatial oscillations that decrease in amplitude with increasing time. The inhomogeneous evolution quickly approaches that found for exact Friedmann universes. We prove a theorem to show that oscillations of $\alpha$ in time (or redshift) cannot occur in Friedmann universes in the BSBM theories considered here.Comment: 7 pages, no figures. Final version: improved discussion and addition of new theorem excluding time oscillation