Critical temperature and the transition from quantum to classical order parameter fluctuations in the three-dimensional Heisenberg antiferromagnet

We present results of extensive quantum Monte Carlo simulations of the three-dimensional (3D) S=1/2 Heisenberg antiferromagnet. Finite-size scaling of the spin stiffness and the sublattice magnetization gives the critical temperature Tc/J = 0.946 +/- 0.001. The critical behavior is consistent with the classical 3D Heisenberg universality class, as expected. We discuss the general nature of the transition from quantum mechanical to classical (thermal) order parameter fluctuations at a continuous Tc > 0 phase transition.Comment: 5 pages, Revtex, 4 PostScript figures include

Stord Orographic Precipitation Experiment (STOPEX): an overview of phase I

STOPEX (Stord Orographic Precipitation Experiment) is a research project of the Geophysical Institute, University of Bergen, Norway, dedicated to the investigation of orographic effects on fine scale precipitation patterns by a combination of numerical modelling and tailored measurement campaigns. Between 24 September and 16 November 2005 the first field campaign STOPEX I has been performed at and around the island of Stord at the west coast of Norway, about 50 km south of Bergen. 12 rain gauges and 3 autonomous weather stations have been installed to measure the variability of precipitation and the corresponding meteorological conditions. This paper gives an overview of the projects motivation, a description of the campaign and a presentation of the precipitation measurements performed. In addition, the extreme precipitation event around 14 November with precipitation amounts up to 240 mm in less than 24 h, is described and briefly discussed. In this context preliminary results of corresponding MM5 simulations are presented, that indicate the problems as well as potential improvement strategies with respect to modelling of fine scale orographic precipitation

Quantum-critical scaling and temperature-dependent logarithmic corrections in the spin-half Heisenberg chain

Low temperature dynamics of the S=1/2 Heisenberg chain is studied via a simple ansatz generalizing the conformal mapping and analytic continuation procedures to correlation functions with multiplicative logarithmic factors. Closed form expressions for the dynamic susceptibility and the NMR relaxation rates 1/T_1 and 1/T_{2G} are obtained, and are argued to improve the agreement with recent experiments. Scaling in q/T and \omega/T are violated due to these logarithmic terms. Numerical results show that the logarithmic corrections are very robust. While not yet in the asymptotic low temperature regime, they provide striking qualitative confirmation of the theoretical results.Comment: 4 pages, RevTex, 4 postscript figures in one fil

Dynamics of the spin-half Heisenberg chain at intermediate temperatures

Combining high-temperature expansions with the recursion method and quantum Monte Carlo simulations with the maximum entropy method, we study the dynamics of the spin-1/2 Heisenberg chain at temperatures above and below the coupling J. By comparing the two sets of calculations, their relative strengths are assessed. At high temperatures, we find that there is a low-frequency peak in the momentum integrated dynamic structure factor, due to diffusive long-wavelength modes. This peak is rapidly suppressed as the temperature is lowered below J. Calculation of the complete dynamic structure factor S(k,w) shows how the spectral features associated with the two-spinon continuum develop at low temperatures. We extract the nuclear spin-lattice relaxation rate 1/T1 from the w-->0 limit, and compare with recent experimental results for Sr2CuO3 and CuGeO3. We also discuss the scaling behavior of the dynamic susceptibility, and of the static structure factor S(k) and the static susceptibility X(k). We confirm the asymptotic low-temperature forms S(pi)~[ln(T)]^(3/2) and X(pi)~T^(-1)[ln(T)]^(1/2), expected from previous theoretical studies.Comment: 15 pages, Revtex, 14 PostScript figures. 2 new figures and related discussion of the recursion method at finite temperature adde

Double-layer Heisenberg antiferromagnet at finite temperature: Brueckner Theory and Quantum Monte Carlo simulations

The double-layer Heisenberg antiferromagnet with intra- and inter-layer couplings $J$ and $J_\perp$ exhibits a zero temperature quantum phase transition between a quantum disordered dimer phase for $g>g_c$ and a Neel phase with long range antiferromagnetic order for $g<g_c$, where $g=J_\perp/J$ and $g_c \approx 2.5$. We consider the behavior of the system at finite temperature for $g \ge g_c$ using two different and complementary approaches; an analytical Brueckner approximation and numerically exact quantum Monte Carlo simulations. We calculate the temperature dependent spin excitation spectrum (including the triplet gap), dynamic and static structure factors, the specific heat, and the uniform magnetic susceptibility. The agreement between the analytical and numerical approaches is excellent. For $T \to 0$ and $g \to g_c$, our analytical results for the specific heat and the magnetic susceptibility coincide with those previously obtained within the nonlinear $\sigma$ model approach for $N\to \infty$. Our quantum Monte Carlo simulations extend to significantly lower temperatures than previously, allowing us to obtain accurate results for the asymptotic quantum critical behavior. We also obtain an improved estimate for the critical coupling: $g_c = 2.525 \pm 0.002$.Comment: 23 pages, 12 figure

Multi-critical point in a diluted bilayer Heisenberg quantum antiferromagnet

The S=1/2 Heisenberg bilayer antiferromagnet with randomly removed inter-layer dimers is studied using quantum Monte Carlo simulations. A zero-temperature multi-critical point (p*,g*) at the classical percolation density p=p* and inter-layer coupling g* approximately 0.16 is demonstrated. The quantum critical exponents of the percolating cluster are determined using finite-size scaling. It is argued that the associated finite-temperature quantum critical regime extends to zero inter-layer coupling and could be relevant for antiferromagnetic cuprates doped with non-magnetic impurities.Comment: 4 pages, 6 figures. v2: only minor changes; accepted for publication in Phys. Rev. Let

Long-range dynamics of magnetic impurities coupled to a two-dimensional Heisenberg antiferromagnet

We consider a two-dimensional Heisenberg antiferromagnet on a square lattice with weakly coupled impurities, i.e. additional spins interacting with the host magnet by a small dimensionless coupling constant g<<1. Using linear spin-wave theory, we find that the magnetization disturbance at distance r from a single impurity behaves as g/r for 1>1/g. Surprisingly the disturbance is inversely proportional to the coupling constant! The interaction between two impurities separated by a distance r is proportional to g^2/r for 1>1/g. Hence at large distances, the interaction is universal and independent of the coupling constant. We also find that the frequency of Rabi oscillations between two impurities is proportional to g^2 ln(gr) at 1<<r<<1/g, logarithmically enhanced compared to the spin-wave width. This leads to a new mechanism for NMR, NQR and EPR line broadening. All these astonishing results are due to the gapless spectrum of the magnetic excitations in the quantum antiferromagnet.Comment: 6 pages, 5 figure

Finite-Size Scaling of the Ground State Parameters of the Two-Dimensional Heisenberg Model

The ground state parameters of the two-dimensional S=1/2 antiferromagnetic Heisenberg model are calculated using the Stochastic Series Expansion quantum Monte Carlo method for L*L lattices with L up to 16. The finite-size results for the energy E, the sublattice magnetization M, the long-wavelength susceptibility chi_perp(q=2*pi/L), and the spin stiffness rho_s, are extrapolated to the thermodynamic limit using fits to polynomials in 1/L, constrained by scaling forms previously obtained from renormalization group calculations for the nonlinear sigma model and chiral perturbation theory. The results are fully consistent with the predicted leading finite-size corrections and are of sufficient accuracy for extracting also subleading terms. The subleading energy correction (proportional to 1/L^4) agrees with chiral perturbation theory to within a statistical error of a few percent, thus providing the first numerical confirmation of the finite-size scaling forms to this order. The extrapolated ground state energy per spin, E=-0.669437(5), is the most accurate estimate reported to date. The most accurate Green's function Monte Carlo (GFMC) result is slightly higher than this value, most likely due to a small systematic error originating from ``population control'' bias in GFMC. The other extrapolated parameters are M=0.3070(3), rho_s = 0.175(2), chi_perp = 0.0625(9), and the spinwave velocity c=1.673(7). The statistical errors are comparable with those of the best previous estimates, obtained by fitting loop algorithm quantum Monte Carlo data to finite-temperature scaling forms. Both M and rho_s obtained from the finite-T data are, however, a few error bars higher than the present estimates. It is argued that the T=0 extrapolations performed here are less sensitive to effects of neglectedComment: 16 pages, RevTex, 9 PostScript figure

Collective effects in spin-crossover chains with exchange interaction

The collective properties of spin-crossover chains are studied. Spin-crossover compounds contain ions with a low-spin ground state and low lying high-spin excited states and are of interest for molecular memory applications. Some of them naturally form one-dimensional chains. Elastic interaction and Ising exchange interaction are taken into account. The transfer-matrix approach is used to calculate the partition function, the fraction of ions in the high-spin state, the magnetization, susceptibility, etc., exactly. The high-spin-low-spin degree of freedom leads to collective effects not present in simple spin chains. The ground-state phase diagram is mapped out and compared to the case with Heisenberg exchange interaction. The various phases give rise to characteristic behavior at nonzero temperatures, including sharp crossovers between low- and high-temperature regimes. A Curie-Weiss law for the susceptibility is derived and the paramagnetic Curie temperature is calculated. Possible experiments to determine the exchange coupling are discussed.Comment: 9 pages, 13 color figures, published versio