How to evaluate ground-state landscapes of spin glasses thermodynamical correctly

Ground states of three-dimensional Ising spin glasses are calculated for sizes up to 14³ using a combination of a genetic algorithm and cluster-exact approximation. For each realization several independent ground states are obtained. Then, by applying ballistic search and T=0Monte-Carlo simulations, it is ensured that each ground state appears with the same probability. Consequently, the results represent the true T=0 thermodynamic behavior. The distribution P(|q|) of overlaps is evaluated. For increasing size the width of P(|q|) and the fraction of the distribution below converge to zero. This indicates that for the infinite system P(|q|) is a delta function, in contrast to previous results. Thus, the ground-state behavior is dominated by few large clusters of similar ground states. Received 17 June 1999     

Metastable states of spin glasses on random thin graphs

In this paper we calculate the mean number of metastable states for spin glasses on so called random thin graphs with couplings taken from a symmetric binary distribution . Thin graphs are graphs where the local connectivity of each site is fixed to some value c. As in totally connected mean field models we find that the number of metastable states increases exponentially with the system size. Furthermore we find that the average number of metastable states decreases as c in agreement with previous studies showing that finite connectivity corrections of order 1/c increase the number of metastable states with respect to the totally connected mean field limit. We also prove that the average number of metastable states in the limit is finite and converges to the average number of metastable states in the Sherrington-Kirkpatrick model. An annealed calculation for the number of metastable states of energy E is also carried out giving a lower bound on the ground state energy of these spin glasses. For small c one may obtain analytic expressions for . Received 14 October 1999 and Received in final form 14 December 1999     

Exact ground states of two-dimensional ±J Ising spin glasses

In this paper we study the problem of finding an exact ground state of a two-dimensional ±J Ising spin glass on a square lattice with nearest neighbor interactions and periodic boundary conditions when there is a concentrationp of negative bonds, withp ranging between 0.1 and 0.9. With our exact algorithm we can determine ground states of grids of sizes up to 50×50 in a moderate amount of computation time (up to 1 hr each) for several values ofp. For the ground-state energy of an infinite spin-glass system withp=0.5 we estimateE _0.5 =–1.4015±0.0008. We report on extensive computational tests based on more than 22,000 experiments.     

Numerical results for spin glass ground states on Bethe lattices: Gaussian bonds

The average ground state energies for spin glasses on Bethe lattices of connectivities r = 3,...,15 are studied numerically for a Gaussian bond distribution. The Extremal Optimization heuristic is employed which provides high-quality approximations to ground states. The energies obtained from extrapolation to the thermodynamic limit smoothly approach the ground-state energy of the Sherrington-Kirkpatrick model for r ↦ ∞. Consistently for all values of r in this study, finite-size corrections are found to decay approximately with ~N^-4/5. The possibility of ~N^-2/3 corrections, found previously for Bethe lattices with a bimodal ± J bond distribution and also for the Sherrington-Kirkpatrick model, are constrained to the additional assumption of very specific higher-order terms. Instance-to-instance fluctuations in the ground state energy appear to be asymmetric up to the limit of the accuracy of our heuristic. The data analysis provides insights into the origin of trivial fluctuations when using continuous bonds and/or sparse networks.     

An NMR approach to the superconducting regime of the spin ladder compound Sr2Ca12Cu24O41

⁶³Cu-NMR experiments of Knight shift and relaxation time T₁ have been performed on the two-leg spin ladders of a Sr₂Ca₁₂Cu₂₄O₄₁ single crystal at several pressures up to the critical pressure for the stabilization of a superconducting ground state. The data confirm the onset of low-lying spin excitations at observed previously [Science 279, 345 (1998)] and reveal a marked decrease of the spin gap under pressures above 20 kbar although a significant fraction of the spin excitations remains gapped at kbar. A comparison between NMR and transport data under pressure suggests that the depression of the spin gap can be ascribed to an increase in the interladder exchange coupling, possibly mediated by the ladder-chain interaction along the b-direction. Received 21 October 1999     

Exact ground states of Ising spin glasses: New experimental results with a branch-and-cut algorithm

In this paper we study two-dimensional Ising spin glasses on a grid with nearest neighbor and periodic boundary interactions, based on a Gaussian bond distribution, and an exterior magnetic field. We show how using a technique called branch and cut, the exact ground states of grids of sizes up to 100×100 can be determined in a moderate amount of computation time, and we report on extensive computational tests. With our method we produce results based on more than 20,000 experiments on the properties of spin glasses whose errors depend only on the assumptions on the model and not on the computational process. This feature is a clear advantage of the method over other, more popular ways to compute the ground state, like Monte Carlo simulation including simulated annealing, evolutionary, and genetic algorithms, that provide only approximate ground states with a degree of accuracy that cannot be determineda priori. Our ground-state energy estimation at zero field is –1.317.     

First excitations of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice

We study the exact low energy spectra of the spin 1/2 Heisenberg antiferromagnet on small samples of the kagomé lattice of up to N=36 sites. In agreement with the conclusions of previous authors, we find that these low energy spectra contradict the hypothesis of Néel type long range order. Certainly, the ground state of this system is a spin liquid, but its properties are rather unusual. The magnetic () excitations are separated from the ground state by a gap. However, this gap is filled with nonmagnetic () excitations. In the thermodynamic limit the spectrum of these nonmagnetic excitations will presumably develop into a gapless continuum adjacent to the ground state. Surprisingly, the eigenstates of samples with an odd number of sites, i.e. samples with an unsaturated spin, exhibit symmetries which could support long range chiral order. We do not know if these states will be true thermodynamic states or only metastable ones. In any case, the low energy properties of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice clearly distinguish this system from either a short range RVB spin liquid or a standard chiral spin liquid. Presumably they are facets of a generically new state of frustrated two-dimensional quantum antiferromagnets. Received: 27 November 1997 / Accepted: 29 January 1998     

Doping-induced spin-manipulation in complex trimer system Ca3Cu3(PO4)4: A density functional investigation

Doping induced spin-manipulation with magnetic (Ni) and non-magnetic (Mg) dopants constitutes the experimental attempts to obtain a singlet ground state system from the linear chain Heisenberg antiferromagnetic Cu-based d⁹ spin-1/2 trimer compound Ca³Cu³(PO⁴)⁴ with doublet ground state. The present study is a density-functional investigation of the effects of such doping on the spin-exchange mechanism and electronic structure of the parent compound. Site-selective doping with zero-spin dopants like Mg is proved to be more efficient than an integral spin dopant Ni in obtaining a spin-gap system with singlet ground state, as also observed in the experimental studies. Doping induced dimerized state is found to be the lowest in ground-state energy. Calculated spin exchange couplings along various possible pathways are observed to attain good agreement with earlier experimental results with suitable optimization of Coulomb repulsion (U) and exchange (J) parameters.     

Slowing down in the three-dimensional three-state Potts glass with nearest neighbor exchange ± J: A Monte Carlo study

,Static and dynamic properties of the Potts model on the simple cubic lattice with nearest neighbor -interaction are obtained from Monte Carlo simulations in a temperature range where full thermal equilibrium still can be achieved (). For a lattice size L = 16, in this range finite size effects are still negligible, but the data for the spin glass susceptibility agree with previous extrapolations based on finite size scaling of very small lattices. While the static properties are compatible with a zero temperature transition, they certainly do not prove it. Unlike the Ising spin glass, the decay of the time-dependent order parameter is compatible with a simple Kohlrausch function, , while a power law prefactor cannot be distinguished. The Kohlrausch exponent y ( T ) decreases from at [0pt] to at [0pt] however. The relaxation time is compatible with the exponential divergence postulated by McMillan for spin glasses at their lower critical dimension, but the exponent that can be extracted still differs significantly from the theoretical value, . Thus the present results support the conclusion that the Potts spin glass in d = 3 dimensions differs qualitatively from the Ising spin glass. Received: 8 October 1997 / Accepted: 27 November 1997     

Doublet and quartet states of Li 2 −

Electronic states of the molecular lithium anion are investigated by configuration-interaction calculations. Comparison with the analogously computed potential energy curves for the lowest singlet and triplet states of the neutral Li₂ shows that in addition to the well-known stable ground state X there also exist metastable excited states of Li ₂ ^- . Within the quartet sector, two candidates for such long-lived states are identified and their spectroscopic properties studied. Received 23 March 1999     

Order by disorder and gaugelike degeneracy in a quantum pyrochlore antiferromagnet

The (three-dimensional) pyrochlore lattice antiferromagnet with Heisenberg spins of large spin length S is a highly frustrated model with a macroscopic degeneracy of classical ground states. The zero-point energy of (harmonic-order) spin-wave fluctuations distinguishes a subset of these states. I derive an approximate but illuminating effective Hamiltonian, acting within the subspace of Ising spin configurations representing the collinear ground states. It consists of products of Ising spins around loops, i.e., has the form of a Z2 lattice gauge theory. The remaining ground-state entropy is still infinite but not extensive, being O(L) for system size O(L3). All these ground states have unit cells bigger than those considered previously.     

The <Emphasis Type="Bold">±</Emphasis><Emphasis Type="Bold">J</Emphasis> spin glass in Migdal-Kadanoff approximation

We study the low-temperature phase of the three-dimensional ± J Ising spin glass in Migdal-Kadanoff approximation. At zero temperature, T = 0, the properties of the spin glass result from the ground-state degeneracy and can be elucidated using scaling arguments based on entropy. The approach to the asymptotic scaling regime is very slow, and the correct exponents are only visible beyond system sizes around 64. At T > 0, a crossover from the zero-temperature behaviour to the behaviour expected from the droplet picture occurs at length scales proportional to T ^-2/ds where d_s is the fractal dimension of a domain wall. Canonical droplet behaviour is not visible at any temperature for systems whose linear dimension is smaller than 16 lattice spacings, because the data are either affected by the zero-temperature behaviour or the critical point behaviour. Received 18 February 2001     

High spin state of Mn in an ideal monolayer on Ag(001)

We studied the magnetic properties of ultra-thin Mn films deposited on Ag (001) held at 80 K with soft X-ray absorption and magnetic circular dichroism. The observed shape and branching ratio of the Mn 2p absorption edge as a function of Mn coverage demonstrate that, up to , the Mn adopts a stable high spin state similar to the Mn atom Hund's rule ⁶ S _5/2 ground state. Above this coverage a rapid transition from localized high spin to itinerant low spin behavior of the Mn 3d electrons is evidenced. Magnetic circular dichroism shows no sign of long range ferromagnetic order in these films at 80 K. The data, first confirm the large atomic-like local magnetic moment, and second are in line with the in-plane antiferromagnetic order, reported recently (Phys. Rev. B 57, 1141 (1998)), for Mn in the nearly ideal on-top Mn monolayer formed by 0.9 ML deposited at 80 K. Received: 4 May 1998     

Theoretical study of vibronic perturbations in magnesium carbide

ABSTRACT

Understanding molecular systems with complex multi-configurational bonding has been of interest to both experimentalists and theoreticians for many years. High level dynamically weighted MRCI calculations were used to generate accurate potential energy curves for the triplet ground state ³Σ^?, and triplet excited states up to (4 ³Σ^?, 4 ³Π and 1 ³Δ) and quintet (1 ⁵Σ^? and 1 ⁵Π) states up to 50,000 cm^?1 above the ground state minimum. The lowest four ³Π states of magnesium mono-carbide (MgC) are strongly coupled leading to lifetimes that are shortened by pre-dissociation for most of the vibronic states. Non-adiabatic derivative couplings between the ³Π states were used to determine diabatic potential energy curves. The state mixing role of spin–orbit coupling, which is much weaker than the non-adiabatic interactions, is discussed. A coupled vibronic Hamiltonian was solved to compute and assign strongly mixed vibronic states. The results are compared and contrasted with the valence iso-electronic beryllium carbide (BeC) system whose results were published earlier [B.J. Barker, I.O. Antonov, J.M. Merritt, V.E. Bondybey, M.C. Heaven, and R. Dawes, J. Chem. Phys. 137, 214313 (2012)]. Transitions, spectroscopic constants and band origins are expected to aid experimental detection of MgC in the future.     

Lifetime measurements in166Er

The lifetimes of five states in the ground band, from spin 6⁺ up to spin 14⁺, and of all even states in the gamma band up to spin 12⁺, have been measured in¹⁶⁶Er using the recoil distance method. The reduced electric quadrupole transition probabilities have been determined from the measured lifetimes using previously measured branching ratios, and the mixing between the ground band and theγ-band has been studied. The transitional electric quadrupole moments for the ground band and theγ-band have been deduced and are discussed.     

Long-range spin-pairing order and spin defects in quantum spin- $${1 \over 2}$$ ladders

For w-legged antiferromagnetic spin-1/2 Heisenberg ladders, a long-range spin pairing order can be identified which enables the separation of the space spanned by finite-range (covalent) valence-bond configurations into w +1 subspaces. Since every subspace has an equivalent counter subspace connected by translational symmetry, twofold degeneracy, breaking translational symmetry is found except for the subspace where the ground state of w = even belongs to. In terms of energy ordering, (non)degeneracy and the discontinuities introduced in the long-range spin pairing order by topological spin defects, the differences between even and odd ladders are explained in a general and systematic way. Received 19 July 1999 and Received in final form 8 October 1999     

Beta decay of 61Ga

The β decay of ⁶¹Ga to its mirror nucleus ⁶¹Zn has been measured for the first time by using on-line mass separation and β-delayed gamma-ray spectroscopy. The observed decay strength to the ground state implies superallowed character in accordance with the systematics of the mirror decays in the sd and fp shell. The β feedings observed to four excited states in ⁶¹Zn are consistent with earlier spin-parity assignments based on in-beam experiments. The ground-state spin and parity for ⁶¹Ga were determined to be 3/2⁻. Received: 28 April 1998 / Revised version: 6 October 1998     

Quantum spin-{3 \over 2} models on the Cayley tree - optimum ground state approach

We present a class of optimum ground states for quantum spin- models on the Cayley tree with coordination number 3. The interaction is restricted to nearest neighbours and contains 5 continuous parameters. For all values of these parameters the Hamiltonian has parity invariance, spin-flip invariance, and rotational symmetry in the xy-plane of spin space. The global ground states are constructed in terms of a 1-parametric vertex state model, which is a direct generalization of the well-known matrix product ground state approach. By using recursion relations and the transfer matrix technique we derive exact analytical expressions for local fluctuations and longitudinal and transversal two-point correlation functions. Received 1 March 1999     

β-delayed proton decays and spin assignments for 140Tb, 141Dy and 143Dy

The proton-rich isotopes ¹⁴⁰Tb and ¹⁴¹Dy were produced via the fusion evaporation reaction ⁴⁰Ca + ¹⁰⁶Cd. Their β-delayed proton decays were studied by p-γ coincidence in combination with a He-jet tape transport system, and half-lives, proton energy spectra, γ-transitions following the proton emission, as well as β-delayed proton branching ratios to the low-lying states in the grand-daughter nuclei were determined. Comparing the experimental data with statistical model calculations, the ground-state spins of ¹⁴⁰Tb and ¹⁴¹Dy were found to be consistent with 7 and 9/2, respectively. The configuration-constrained nuclear potential energy surfaces (NPES) of ¹⁴⁰Tb and ¹⁴¹Dy were calculated using the Woods-Saxon-Strutinsky method, which suggest the ground-state spins and parities of ¹⁴⁰Tb and ¹⁴¹Dy to be 7⁺ and 9/2^-, respectively. In addition, the configuration-constrained NPES of ¹⁴³Dy were calculated, which predict a 1/2⁺ ground state and a 11/2^- isomer with excitation energy of 198keV. These findings are consistent with our previous experimental data on ¹⁴³Dy reported in Eur. Phys. J. A 16, 347 (2003).     

On evaluation of transverse spin fluctuations in quantum magnets

A numerical method is described for evaluating transverse spin correlations in the random phase approximation. Quantum spin-fluctuation corrections to sublattice magnetization are evaluated for the antiferromagnetic ground state of the half-filled Hubbard model in two and three dimensions in the whole U/t range. Extension to the case of defects in the AF is also discussed for spin vacancies and low-U impurities. In the limit, the vacancy-induced enhancement in the spin fluctuation correction is obtained for the spin-vacancy problem in two dimensions, for vacancy concentration up to the percolation threshold. For low-U impurities, the overall spin fluctuation correction is found to be strongly suppressed, although surprisingly spin fluctuations are locally enhanced at the low-U sites. Received 27 April 1998 and Received in final form 13 August 1998