Interaction effects between impurities in low dimensional spin-1/2 antiferromagnets

We are considering the interplay between several non-magnetic impurities in the spin-1/2 Heisenberg antiferromagnet in chains, ladders and planes by introducing static vacancies in numerical quantum Monte Carlo simulations. The effective potential between two and more impurities is accurately determined, which gives a direct measure of the quantum correlations in the systems. Large effective interaction potentials are an indication of strong quantum correlations in the system and reflect the detailed nature of the valence bond ground states. In two-dimensions (2D) the interactions are smaller, but can still be analyzed in terms of valence bonds.Comment: 8 pages, 6 figures, accepted by Europhys. Lett. The latest pdf file is available at http://www.physik.uni-kl.de/eggert/papers/interact2d.pd

Is Neolithic land use correlated with demography? An evaluation of pollen-derived land cover and radiocarbon-inferred demographic change from Central Europe

The transformation of natural landscapes in Middle Europe began in the Neolithic as a result of the introduction of food-producing economies. This paper examines the relation between land-cover and demographic change in a regionally restricted case study. The study area is the Western Lake Constance area which has very detailed palynological as well as archaeological records. We compare land-cover change derived from nine pollen records using a pseudo-biomisation approach with 14C date probability density functions from archaeological sites which serve as a demographic proxy. We chose the Lake Constance area as a regional example where the pollen signal integrates a larger spatial pattern. The land-cover reconstructions for this region show first notable impacts at the Middle to Young Neolithic transition. The beginning of the Bronze Age is characterised by increases of arable land and pasture/meadow, whereas the deciduous woodland decreases dramatically. Changes in the land-cover classes show a correlation with the 14C density curve: the correlation is best with secondary woodland in the Young Neolithic which reflects the lake shore settlement dynamics. In the Early Bronze Age, the radiocarbon density correlates with open land-cover classes, such as pasture, meadow and arable land, reflecting a change in the land-use strategy. The close overall correspondence between the two archives implies that population dynamics and land-cover change were intrinsically linked. We therefore see human impact as a key driver for vegetation change in the Neolithic. Climate might have an influence on vegetation development, but the changes caused by human land use are clearly detectable from Neolithic times, at least in these densely settled, mid-altitude landscapes

Numerical Study of a Two-Dimensional Quantum Antiferromagnet with Random Ferromagnetic Bonds

A Monte Carlo method for finite-temperature studies of the two-dimensional quantum Heisenberg antiferromagnet with random ferromagnetic bonds is presented. The scheme is based on an approximation which allows for an analytic summation over the realizations of the randomness, thereby significantly alleviating the ``sign problem'' for this frustrated spin system. The approximation is shown to be very accurate for ferromagnetic bond concentrations of up to ten percent. The effects of a low concentration of ferromagnetic bonds on the antiferromagnetism are discussed.Comment: 11 pages + 5 postscript figures (included), Revtex 3.0, UCSBTH-94-2

Quantum Phase Transition of Randomly-Diluted Heisenberg Antiferromagnet on a Square Lattice

Ground-state magnetic properties of the diluted Heisenberg antiferromagnet on a square lattice are investigated by means of the quantum Monte Carlo method with the continuous-time loop algorithm. It is found that the critical concentration of magnetic sites is independent of the spin size S, and equal to the two-dimensional percolation threshold. However, the existence of quantum fluctuations makes the critical exponents deviate from those of the classical percolation transition. Furthermore, we found that the transition is not universal, i.e., the critical exponents significantly depend on S.Comment: RevTeX, 4 pages including 5 EPS figure

Classical Correlation-Length Exponent in Non-Universal Quantum Phase Transition of Diluted Heisenberg Antiferromagnet

Critical behavior of the quantum phase transition of a site-diluted Heisenberg antiferromagnet on a square lattice is investigated by means of the quantum Monte Carlo simulation with the continuous-imaginary-time loop algorithm. Although the staggered spin correlation function decays in a power law with the exponent definitely depending on the spin size $S$, the correlation-length exponent is classical, i.e., $\nu=4/3$. This implies that the length scale characterizing the non-universal quantum phase transition is nothing but the mean size of connected spin clusters.Comment: 4 pages, 3 figure

Disorder Induced Phase Transition in a Random Quantum Antiferromagnet

A two-dimensional Heisenberg model with random antiferromagnetic nearest-neighbor exchange is studied using quantum Monte Carlo techniques. As the strength of the randomness is increased, the system undergoes a transition from an antiferromagnetically ordered ground state to a gapless disordered state. The finite-size scaling of the staggered structure factor and susceptibility is consistent with a dynamic exponent $z = 2$.Comment: Revtex 3.0, 10 pages + 5 postscript figures available upon request, UCSBTH-94-1

Rare region effects at classical, quantum, and non-equilibrium phase transitions

Rare regions, i.e., rare large spatial disorder fluctuations, can dramatically change the properties of a phase transition in a quenched disordered system. In generic classical equilibrium systems, they lead to an essential singularity, the so-called Griffiths singularity, of the free energy in the vicinity of the phase transition. Stronger effects can be observed at zero-temperature quantum phase transitions, at nonequilibrium phase transitions, and in systems with correlated disorder. In some cases, rare regions can actually completely destroy the sharp phase transition by smearing. This topical review presents a unifying framework for rare region effects at weakly disordered classical, quantum, and nonequilibrium phase transitions based on the effective dimensionality of the rare regions. Explicit examples include disordered classical Ising and Heisenberg models, insulating and metallic random quantum magnets, and the disordered contact process.Comment: Topical review, 68 pages, 14 figures, final version as publishe