Rain: Relaxations in the sky

We demonstrate how, from the point of view of energy flow through an open system, rain is analogous to many other relaxational processes in Nature such as earthquakes. By identifying rain events as the basic entities of the phenomenon, we show that the number density of rain events per year is inversely proportional to the released water column raised to the power 1.4. This is the rain-equivalent of the Gutenberg-Richter law for earthquakes. The event durations and the waiting times between events are also characterised by scaling regions, where no typical time scale exists. The Hurst exponent of the rain intensity signal $H = 0.76 > 0.5$. It is valid in the temporal range from minutes up to the full duration of the signal of half a year. All of our findings are consistent with the concept of self-organised criticality, which refers to the tendency of slowly driven non-equilibrium systems towards a state of scale free behaviour.Comment: 9 pages, 8 figures, submitted to PR

Astrophysical S-factors for fusion reactions involving C, O, Ne and Mg isotopes

Using the Sao Paulo potential and the barrier penetration formalism we have calculated the astrophysical factor S(E) for 946 fusion reactions involving stable and neutron-rich isotopes of C, O, Ne, and Mg for center-of-mass energies E varying from 2 MeV to 18-30 MeV (covering the range below and above the Coulomb barrier). We have parameterized the energy dependence S(E) by an accurate universal 9-parameter analytic expression and present tables of fit parameters for all the reactions. We also discuss the reduced 3-parameter version of our fit which is highly accurate at energies below the Coulomb barrier, and outline the procedure for calculating the reaction rates. The results can be easily converted to thermonuclear or pycnonuclear reaction rates to simulate various nuclear burning phenomena, in particular, stellar burning at high temperatures and nucleosynthesis in high density environments.Comment: 30 pages including 11 tables, 4 figures, ADNDT, accepte

Elementary excitations of the symmetric spin-orbital model: The XY limit

The elementary excitations of the 1D, symmetric, spin-orbital model are investigated by studying two anisotropic versions of the model, the pure XY and the dimerized XXZ case, with analytical and numerical methods. While they preserve the symmetry between spin and orbital degrees of freedom, these models allow for a simple and transparent picture of the low--lying excitations: In the pure XY case, a phase separation takes place between two phases with free--fermion like, gapless excitations, while in the dimerized case, the low-energy effective Hamiltonian reduces to the 1D Ising model with gapped excitations. In both cases, all the elementary excitations involve simultaneous flips of the spin and orbital degrees of freedom, a clear indication of the breakdown of the traditional mean-field theory.Comment: Revtex, two figure

Finite-size Scaling of Correlation Ratio and Generalized Scheme for the Probability-Changing Cluster Algorithm

We study the finite-size scaling (FSS) property of the correlation ratio, the ratio of the correlation functions with different distances. It is shown that the correlation ratio is a good estimator to determine the critical point of the second-order transition using the FSS analysis. The correlation ratio is especially useful for the analysis of the Kosterlitz-Thouless (KT) transition. We also present a generalized scheme of the probability-changing cluster algorithm, which has been recently developed by the present authors, based on the FSS property of the correlation ratio. We investigate the two-dimensional quantum XY model of spin 1/2 with this generalized scheme, obtaining the precise estimate of the KT transition temperature with less numerical effort.Comment: 4 pages, RevTeX4, to appear in Phys. Rev. B, Rapid Communication

Thermodynamics of the one-dimensional SU(4) symmetric spin-orbital model

The ground state properties and the thermodynamics of the one-dimensional SU(4) symmetric spin system with orbital degeneracy are investigated using the quantum Monte Carlo loop algorithm. The spin-spin correlation functions exhibit a 4-site periodicity, and their low temperature behavior is controlled by two correlation lengths that diverge like the inverse temperature, while the entropy is linear in temperature and its slope is consistent with three gapless modes of velocity $\pi/2$. The physical implications of these results are discussed.Comment: 4 pages, 4 figures, RevTe

Critical exponents of the quantum phase transition in a planar antiferromagnet

We have performed a large scale quantum Monte Carlo study of the quantum phase transition in a planar spin-1/2 Heisenberg antiferromagnet with CaV4O9 structure. We obtain a dynamical exponent z=1.018+/-0.02. The critical exponents beta, nu and eta agree within our errors with the classical 3D O(3) exponents, expected from a mapping to the nonlinear sigma model. This confirms the conjecture of Chubukov, Sachdev and Ye [Phys. Rev. B 49, 11919 (1994)] that the Berry phase terms in the planar Heisenberg antiferromagnet are dangerously irrelevant.Comment: 5 pages including 4 figures; revised version: some minor changes and added reference

Spin correlations in an isotropic spin-5/2 two-dimensional antiferromagnet

We report a neutron scattering study of the spin correlations for the spin 5/2, two-dimensional antiferromagnet Rb_2MnF_4 in an external magnetic field. Choosing fields near the system's bicritical point, we tune the effective anisotropy in the spin interaction to zero, constructing an ideal S=5/2 Heisenberg system. The correlation length and structure factor amplitude are closely described by the semiclassical theory of Cuccoli et al. over a broad temperature range but show no indication of approaching the low-temperature renormalized classical regime of the quantum non-linear sigma model.Comment: 4 pages, 3 EPS figure

Ground state parameters, finite-size scaling, and low-temperature properties of the two-dimensional S=1/2 XY model

We present high-precision quantum Monte Carlo results for the S=1/2 XY model on a two-dimensional square lattice, in the ground state as well as at finite temperature. The energy, the spin stiffness, the magnetization, and the susceptibility are calculated and extrapolated to the thermodynamic limit. For the ground state, we test a variety of finite-size scaling predictions of effective Lagrangian theory and find good agreement and consistency between the finite-size corrections for different quantities. The low-temperature behavior of the susceptibility and the internal energy is also in good agreement with theoretical predictions.Comment: 6 pages, 8 figure