Low-energy parameters and spin gap of a frustrated spin-ss Heisenberg antiferromagnet with s≤32s \leq \frac{3}{2} on the honeycomb lattice

The coupled cluster method is implemented at high orders of approximation to investigate the zero-temperature $(T=0)$ phase diagram of the frustrated spin-$s$ $J_{1}$--$J_{2}$--$J_{3}$ antiferromagnet on the honeycomb lattice. The system has isotropic Heisenberg interactions of strength $J_{1}>0$, $J_{2}>0$ and $J_{3}>0$ between nearest-neighbour, next-nearest-neighbour and next-next-nearest-neighbour pairs of spins, respectively. We study it in the case $J_{3}=J_{2}\equiv \kappa J_{1}$, in the window $0 \leq \kappa \leq 1$ that contains the classical tricritical point (at $\kappa_{{\rm cl}}=\frac{1}{2}$) of maximal frustration, appropriate to the limiting value $s \to \infty$ of the spin quantum number. We present results for the magnetic order parameter $M$, the triplet spin gap $\Delta$, the spin stiffness $\rho_{s}$ and the zero-field transverse magnetic susceptibility $\chi$ for the two collinear quasiclassical antiferromagnetic (AFM) phases with N\'{e}el and striped order, respectively. Results for $M$ and $\Delta$ are given for the three cases $s=\frac{1}{2}$, $s=1$ and $s=\frac{3}{2}$, while those for $\rho_{s}$ and $\chi$ are given for the two cases $s=\frac{1}{2}$ and $s=1$. On the basis of all these results we find that the spin-$\frac{1}{2}$ and spin-1 models both have an intermediate paramagnetic phase, with no discernible magnetic long-range order, between the two AFM phases in their $T=0$ phase diagrams, while for $s > 1$ there is a direct transition between them. Accurate values are found for all of the associated quantum critical points. While the results also provide strong evidence for the intermediate phase being gapped for the case $s=\frac{1}{2}$, they are less conclusive for the case $s=1$. On balance however, at least the transition in the latter case at the striped phase boundary seems to be to a gapped intermediate state

The DSUBmm Approximation Scheme for the Coupled Cluster Method and Applications to Quantum Magnets

A new approximate scheme, DSUB$m$, is described for the coupled cluster method. We then apply it to two well-studied (spin-1/2 Heisenberg antiferromagnet) spin-lattice models, namely: the $XXZ$ and the $XY$ models on the square lattice in two dimensions. Results are obtained in each case for the ground-state energy, the sublattice magnetization and the quantum critical point. They are in good agreement with those from such alternative methods as spin-wave theory, series expansions, quantum Monte Carlo methods and those from the CCM using the LSUB$m$ scheme.Comment: 18 pages, 10 figure

Firewood, food and niche construction : the potential role of Mesolithic hunter-gatherers in actively structuring Scotland's woodlands.

Over the past few decades the potential role of Mesolithic hunter–gatherers in actively constructing their own niches, through the management of wild plants, has frequently been discussed. It is probable that Mesolithic hunter–gatherers systematically exploited specific woodland resources for food and fuel and influenced the ‘natural’ abundance or distribution of particular species within Mesolithic environments. Though there has been considerable discussion of the pollen evidence for potential small-scale human-woodland manipulation in Mesolithic Scotland, the archaeobotanical evidence for anthropogenic firewood and food selection has not been discussed in this context. This paper assesses the evidence for the active role of Mesolithic hunter–gatherer communities in systematically exploiting and managing woodlands for food and fuel in Scotland. While taphonomic factors may have impacted on the frequency of specific species in archaeobotanical assemblages, it is suggested that hunter–gatherers in Mesolithic Scotland were systematically using woodland plants, and in particular hazel and oak, for food and fuel. It is argued that the pollen evidence for woodland management is equivocal, but hints at the role of hunter–gatherers in shaping the structure of their environments, through the maintenance or creation of woodland clearings for settlement or as part of vegetation management strategies. It is proposed that Mesolithic hunter–gatherers may have actively contributed to niche construction and that the systematic use of hazel and oak as a fuel may reflect the deliberate pruning of hazel trees to increase nut-yields and the inadvertent – or perhaps deliberate – coppicing of hazel and oak during greenwood collection

Phase Transitions in the Spin-Half J_1--J_2 Model

The coupled cluster method (CCM) is a well-known method of quantum many-body theory, and here we present an application of the CCM to the spin-half J_1--J_2 quantum spin model with nearest- and next-nearest-neighbour interactions on the linear chain and the square lattice. We present new results for ground-state expectation values of such quantities as the energy and the sublattice magnetisation. The presence of critical points in the solution of the CCM equations, which are associated with phase transitions in the real system, is investigated. Completely distinct from the investigation of the critical points, we also make a link between the expansion coefficients of the ground-state wave function in terms of an Ising basis and the CCM ket-state correlation coefficients. We are thus able to present evidence of the breakdown, at a given value of J_2/J_1, of the Marshall-Peierls sign rule which is known to be satisfied at the pure Heisenberg point (J_2 = 0) on any bipartite lattice. For the square lattice, our best estimates of the points at which the sign rule breaks down and at which the phase transition from the antiferromagnetic phase to the frustrated phase occurs are, respectively, given (to two decimal places) by J_2/J_1 = 0.26 and J_2/J_1 = 0.61.Comment: 28 pages, Latex, 2 postscript figure

Frustrated spin-12\frac{1}{2} Heisenberg magnet on a square-lattice bilayer: High-order study of the quantum critical behavior of the J1J_{1}--J2J_{2}--J1⊥J_{1}^{\perp} model

The zero-temperature phase diagram of the spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{1}^{\perp}$ model on an $AA$-stacked square-lattice bilayer is studied using the coupled cluster method implemented to very high orders. Both nearest-neighbor (NN) and frustrating next-nearest-neighbor Heisenberg exchange interactions, of strengths $J_{1}>0$ and $J_{2} \equiv \kappa J_{1}>0$, respectively, are included in each layer. The two layers are coupled via a NN interlayer Heisenberg exchange interaction with a strength $J_{1}^{\perp} \equiv \delta J_{1}$. The magnetic order parameter $M$ (viz., the sublattice magnetization) is calculated directly in the thermodynamic (infinite-lattice) limit for the two cases when both layers have antiferromagnetic ordering of either the N\'{e}el or the striped kind, and with the layers coupled so that NN spins between them are either parallel (when $\delta 0$) to one another. Calculations are performed at $n$th order in a well-defined sequence of approximations, which exactly preserve both the Goldstone linked cluster theorem and the Hellmann-Feynman theorem, with $n \leq 10$. The sole approximation made is to extrapolate such sequences of $n$th-order results for $M$ to the exact limit, $n \to \infty$. By thus locating the points where $M$ vanishes, we calculate the full phase boundaries of the two collinear AFM phases in the $\kappa$--$\delta$ half-plane with $\kappa > 0$. In particular, we provide the accurate estimate, ($\kappa \approx 0.547,\delta \approx -0.45$), for the position of the quantum triple point (QTP) in the region $\delta < 0$. We also show that there is no counterpart of such a QTP in the region $\delta > 0$, where the two quasiclassical phase boundaries show instead an ``avoided crossing'' behavior, such that the entire region that contains the nonclassical paramagnetic phases is singly connected

Validation of empirical measures of welfare change: comment

In an excellent article from a recent issue of this journal, Sellar, Stoll and Chavas (1985) make a technical error which causes them to misstate their closed-ended estimates of willingness to pay. Truncation of the estimated cummulative distribution function must we made explicit in compution of willingness to pay.nonmarket valuation; contingent valuation; stated preferences; welfare evaluation; willingness to pay