Form of the long-range potential observed in fast-neutron scattering by heavy nuclei

It is shown that the discrepancy between the results obtained for different neutron-energy ranges, when the neutron polarizability is derived from data on neutron scattering, can be removed if one assumes that a strong-interaction long-range potential of van der Waals (～r ^?6) or of Casimir and Polder (～r ^?7) is observed in fast-neutron scattering. This strong-interaction long-range potential possibly has some experimental confirmation in elastic pp scattering.     

High-spin states in 166Lu

It is shown that the discrepancy between the results obtained for different neutron energy ranges, when neutron polarizability is derived from the neutron scattering data, can be removed if one assumes that at the fast neutron scattering a strong-interaction long-range potential of Van der Waals (～ r ^?6 ) or Casimir-Polder (～ r ^?7 ) is observed. This strong-interaction long-range potential has possibly some experimental confirmation in the elastic p-p scattering.     

Long-range connections, quantum magnets and dilute contact processes

In this article, we briefly review the critical behaviour of a long-range percolation model in which any two sites are connected with a probability that falls off algebraically with the distance. The results of this percolation transition are used to describe the quantum phase transitions in a dilute transverse Ising model at the percolation threshold p_c of the long-range connected lattice. In the similar spirit, we propose a new model of a contact process defined on the same long-range diluted lattice and explore the transitions at p_c. The long-range nature of the percolation transition allows us to evaluate some critical exponents exactly in both the above models. Moreover, mean field theory is valid for a wide region of parameter space. In either case, the strength of Griffiths McCoy singularities are tunable as the range parameter is varied.     

A non-extensive statistical physics approach to the polarity reversals of the geomagnetic field

Using the CK95 database of Cande and Kent (1995) [7], we apply the concepts of non-extensive statistical physics (NESP) to the time intervals between two consecutive geomagnetic reversals, called inter-reversal times. The application of NESM is appropriate to systems such as the geomagnetic field where non-linearity, long-range interactions, memory effects and scaling are important. We calculate the probability density function for the inter-reversal times and using the CK95 geomagnetic reversals and we estimate a thermodynamic q parameter of q=1.5, which supports the conclusion that the geomagnetic system is a sub-extensive one with long-range memory effects. The results discussed using the complementary to the NESP approach of superstatistics which is based on a superposition of ordinary local equilibrium statistical mechanics, using a suitable intensive parameter β that fluctuates on a relatively large temporal scale, leading to the conclusion that two degrees of freedom describe the process which generates the geomagnetic reversals.     

Geometry effect on the magnetic ordering of geometrically frustrated rectangular and triangular magnets

We investigate the effect of geometry on the ground-state ordering of artificially frustrated magnetic rectangular and triangular lattices by Monte Carlo method. By varying the vertical lattice spacing while keeping the horizontal one fixed, we show that when the ratio of vertical to horizontal lattice spacing, labeled by η, is less than 1.82, the ground state of the rectangular lattice presents long-range antiferromagnetic order and for η?1.82 the ground state changes to long-range mixed ferromagnetic and antiferromagnetic order. For the frustrated triangular lattice, the short-range ordered state as well as two long-range ordered ground states occurs transiently at η=0.87 and 2, where the energies of the two ground states with long-range order are approximately equal. In addition, the level of frustration of both frustrated lattices is found to be largely relevant to the ratio η.     

Long-range Jastrow correlations

We develop a promising many-body method to evaluate the equation of state for dense neutron matter and liquid helium. The ground state of the Fermi fluid is described by a conventional Jastrow ansatz. We admit the presence of short- and long-range correlations. Under this assumption we study the generating function which has been introduced by Wu and Feenberg. We employ a graphic formulation and develop the diagrammatic expansion of the generating function and the radial distribution function. If long-range correlations are assumed, the diagrams have singular parts. We give a proof that the total contribution of such diagrams to the generating function which contain two, three, and four correlation lines is of finite value. The same property is shown for a selected class of singular diagrams containing α correlation lines (α>4). To verify the cancellation phenomenon we introduce a two-body function which serves graphically as an insertion into selected singular diagrams. For the remaining classes of diagrams we need three-, four-, ?, n-body insertions. The result is cast into the form of a theorem. The cancellation rests on the exclusion principle and does not depend on the special shape of the correlation function. Finally, a generalized hypernetted-chain summation of diagrams which represent the radial distribution function is executed. The procedure includes exchange contributions and can be employed if short-and/or long-range correlations are present.     

A new theoretical constraint on the static critical behaviour of the specific heat

We show from a field-theoretical approach that, if we admit that the additive renormalization function of the specific heat C is singular at the fixed point, we obtain a coherent formulation of the critical behaviour of C. Especially we show that the α<0 case, which corresponds to a cusp for C, is dominated by a critical constant B_cr generated by the long-range correlations of the fluctuations. We derive a universal combination between the leading and first correction amplitudes and B_cr, which will have a great importance in the analysis of experimental data.     

Power law and multiscaling properties of the Chinese stock market

We investigate the cumulative probability density function (PDF) and the multiscaling properties of the returns in the Chinese stock market. By using returns data adjusted for thin trading, we find that the distribution has power-law tails at shorter microscopic timescales or lags. However, the distribution follows an exponential law for longer timescales. Furthermore, we investigate the long-range correlation and multifractality of the returns in the Chinese stock market by the DFA and MFDFA methods. We find that all the scaling exponents are between 0.5 and 1 by DFA method, which exhibits the long-range power-law correlations in the Chinese stock market. Moreover, we find, by MFDFA method, that the generalized Hurst exponents h(q) are not constants, which shows the multifractality in the Chinese stock market. We also find that the correlation of Shenzhen stock market is stronger than that of Shanghai stock market.     

Conducting to non-conducting transition in dual transmission lines using a ternary model with long-range correlated disorder

In this work we study the behavior of the allowed and forbidden frequencies in disordered classical dual transmission lines when the values of capacitances {Cj} are distributed according to a ternary model with long-range correlated disorder. We introduce the disorder from a random sequence with a power spectrum S(k)∝k−(2α−1), where α?0.5 is the correlation exponent. From this sequence we generate an asymmetric ternary map using two map parameters b₁ and b₂, which adjust the occupancy probability of each possible value of the capacitances Cj={CA,CB,CC,}. If the sequence of capacitance values is totally at random α=0.5 (white noise), the electrical transmission line is in the non-conducting state for every frequency ω. When we introduce long-range correlations in the distribution of capacitances, the electrical transmission lines can change their conducting properties and we can find a transition from the non-conducting to conducting state for a fixed system size. This implies the existence of critical values of the map parameters for each correlation exponent α. By performing finite-size scaling we obtain the asymptotic value of the map parameters in the thermodynamic limit for any α. With these data we obtain a phase diagram for the symmetric ternary model, which separates the non-conducting state from the conducting one. This is the fundamental result of this Letter. In addition, introducing one or more impurities in random places of the long-range correlated distribution of capacitances, we observe a dramatic change in the conducting properties of the electrical transmission lines, in such a way that the system jumps from conducting to non-conducting states. We think that this behavior can be considered as a possible mechanism to secure communication.     

Magnetic properties of MnxMg1-xS solid solutions

The static magnetic properties of the polycrystalline solid solutions Mn_xMg_1-xS(0<x?1) are reported. The experimental data reveal the appearance of a critical concentration x_c=0.13±0.01 for long-range magnetic ordering, which is in good agreement with the result of a series expansion of the mean cluster size for a face-centered cubic lattice with exchange interactions up to 12 nearest neighbours and 6 next-nearest neighbours. At concentrations far below x_c the existence of long-range exchange interactions is demonstrated.     

Phase transitions in the 2D J 1-J 2 Heisenberg model with arbitrary signs of exchange interactions

The ground state of the J ₁-J ₂ Heisenberg model with arbitrary signs of exchange is studied for spin S = 1/2 in the case of the two-dimensional (2D) square lattice. The states with different types of spin long-range order (antiferromagnetic checkerboard, stripe, collinear ferromagnetic) as well as the disordered spin liquid states are described in the framework of one analytical approach. In particular, it is shown that the phase transition between the ferromagnetic spin liquid and the ferromagnet with long-range order is of the second order. In the vicinity of such transition, we have found the ferromagnetic state with a rapidly varying condensate function.     

Density functional theory description of the mechanism of ferromagnetism in nitrogen-doped SnO2

Based on first-principles calculations, we have studied the occurrence of spin polarization in the magnetic metal oxide SnO₂ doped with nonmagnetic nitrogen (N) impurities. It was found that the local magnetic moments are localized mainly on the N dopant, causing a total moment of 0.95μB per cell. The long-range magnetic coupling of N-doped SnO₂ may be attributed to a p-p coupling interaction between the N impurity and host valence states.     

Detecting long-range correlations in fire sequences with Detrended fluctuation analysis

The spatial-temporal power-law distributions are found in many natural systems, which have self-similarity and fractal behavior. By analyzing the time series of such systems, we could expect to explore and understand the underlying mechanisms. In this paper, the Detrended fluctuation analysis (DFA) is used to analyze the long-range correlations of forest and urban fires in Japan and China. It is found that the interevent time series of both forest and urban fires have the persistent long-range power-law correlations, and they all have two scaling exponents, α₁ and α₂, which are both bigger than 0.5 and smaller than 1.0, despite the different regions and countries. For forest fires, 0.61<α₁<0.73,0.87<α₂<0.98 and for urban fires, 0.52<α₁<0.61,0.59<α₂<0.88. The result suggests that fires have self-similarity characteristics. The occurrence of forest fires may have connection with the weather fluctuations, which have significant effects on the ignition and have the similar temporal correlations. It is shown that the interval sequences of urban fires closely resemble that of white noise in small timescale, and the correlations are weaker than that of forest fires. Human behavior and human density may affect the long-range correlation in some way. This seems to be helpful to understand the complexity of fire system in temporal aspect.     

Quasi-periodic breathers in Hamiltonian networks of long-range coupling

This work is concerned with Hamiltonian networks of weakly and long-range coupled oscillators with either variable or constant on-site frequencies. We derive an infinite dimensional KAM-like theorem by which we establish that, given any N-sites of the lattice, there is a positive measure set of small amplitude, quasi-periodic breathers (solutions of the Hamiltonian network that are quasi-periodic in time and exponentially localized in space) having N-frequencies which are only slightly deformed from the on-site frequencies.     

Conducting properties of classical transmission lines with Ornstein-Uhlenbeck type disorder

In this work we study the behavior of bands of extended states and localized states which appear in classical disordered electrical transmission lines, when we use a ternary map and the Ornstein-Uhlenbeck process to generate the long-range correlated disorder, instead of using the Fourier filtering method. By performing finite-size scaling we obtain the asymptotic value of the map parameter b in the thermodynamic limit in a selected range of values of the parameters γ and C of the Ornstein-Uhlenbeck process. With these data we obtain the phase diagrams which separate the localized states from the extended states. These are the fundamental results of this article.     

Spin degrees of freedom and flattening of the spectra of single-particle excitations in strongly correlated Fermi systems

The impact of long-range spin-spin correlations on the structure of a flat portion in single-particle spectra ξ(p), which emerges beyond the point where the Landau state loses its stability, is studied. We supplement the well-known Nozieres model of a Fermi system with limited scalar long-range forces by a similar long-range spin-dependent term and calculate the spectra versus its strength g. It is found that Nozieres' results hold as long as g>0. However, with g changing its sign, the spontaneous magnetization is shown to arise at any nonzero g. The increase in the strength |g| is demonstrated to result in shrinkage of the domain in momentum space, occupied by the flat portion of ξ(p), and, eventually, in its vanishing.     

An exactly solvable many-body problem in one dimension and the short-range Dyson model

For N impenetrable particles in one dimension with upto next-to-nearest neighbours interaction, we obtain the exact ground state.We establish a mapping between these N-body problems and the short-range Dyson model introduced recently to model intermediate spectral statistics. We prove the absence of long-range order and off-diagonal long-range order in the corresponding many-body theory.     

Hamiltonian and Brownian systems with long-range interactions: III. The BBGKY hierarchy for spatially inhomogeneous systems

We study the growth of correlations in systems with weak long-range interactions. Starting from the BBGKY hierarchy, we determine the evolution of the two-body correlation function by using an expansion of the solutions of the hierarchy in powers of 1/N in a proper thermodynamic limit N→+∞, where N is the number of particles. These correlations are responsible for the “collisional” evolution of the system beyond the Vlasov regime due to finite N effects. We obtain a general kinetic equation that can be applied to spatially inhomogeneous systems and that takes into account memory effects. These peculiarities are specific to systems with unshielded long-range interactions. For spatially homogeneous systems with short memory time like plasmas, we recover the classical Landau (or Lenard-Balescu) equations. An interest of our approach is to develop a formalism that remains in physical space (instead of Fourier space) and that can deal with spatially inhomogeneous systems. This enlightens the basic physics and provides novel kinetic equations with a clear physical interpretation. However, unless we restrict ourselves to spatially homogeneous systems, closed kinetic equations can be obtained only if we ignore some collective effects between particles. General exact coupled equations taking into account collective effects are also given. We use this kinetic theory to discuss the processes of violent collisionless relaxation and slow collisional relaxation in systems with weak long-range interactions. In particular, we investigate the dependence of the relaxation time with the system size N and try to provide a coherent discussion of all the numerical results obtained for these systems.     

Intermittent criticality in the long-range connective sandpile (LRCS) model

We here propose a long-range connective sandpile model with variable connection probability Pc which has an important impact on the slope of the power-law frequency-size distribution of avalanches. The long-range connection probability Pc is changed according to an explicit function of the size of the latest event, although the evolution rule of Pc may be different in various physical systems. Such version of the sandpile model demonstrates large fluctuations in the dynamical variable 〈Z〉(t) (the spatially averaged amount of grains retained within the grid at each time step), indicating the state of intermittent criticality in the system. Many researches have suggested that the earthquake fault system is an intermittent criticality system, which would imply some level of statistical predictability of great events. Our modified sandpile model thus provides a testing ground for many proposed precursory measures related to great earthquakes.