Direct sampling of complex landscapes at low temperatures: the three-dimensional +/-J Ising spin glass

A method is presented, which allows to sample directly low-temperature configurations of glassy systems, like spin glasses. The basic idea is to generate ground states and low lying excited configurations using a heuristic algorithm. Then, with the help of microcanonical Monte Carlo simulations, more configurations are found, clusters of configurations are determined and entropies evaluated. Finally equilibrium configuration are randomly sampled with proper Gibbs-Boltzmann weights. The method is applied to three-dimensional Ising spin glasses with +- J interactions and temperatures T<=0.5. The low-temperature behavior of this model is characterized by evaluating different overlap quantities, exhibiting a complex low-energy landscape for T>0, while the T=0 behavior appears to be less complex.Comment: 9 pages, 7 figures, revtex (one sentence changed compared to v2

Spin Models on Thin Graphs

We discuss the utility of analytical and numerical investigation of spin models, in particular spin glasses, on ordinary ``thin'' random graphs (in effect Feynman diagrams) using methods borrowed from the ``fat'' graphs of two dimensional gravity. We highlight the similarity with Bethe lattice calculations and the advantages of the thin graph approach both analytically and numerically for investigating mean field results.Comment: Contribution to Parallel Session at Lattice95, 4 pages. Dodgy compressed ps file replaced with uuencoded LaTex original + ps figure

SrCu_2(BO_3)_2 - a Two Dimensional Spin Liquid

We study an extended Shastry-Sutherland model for SrCu_2(BO_3)_2 and analyze the low lying parts of the energy spectrum by means of a perturbative unitary transformation based on flow equations. The derivation of the 1-magnon dispersion (elementary triplets) is discussed. Additionally, we give a quantitative description (symmetries and energies) of bound states made from two elementary triplets. Our high order results allow to fix the model parameters for SrCu_2(BO_3)_2 precisely: J_1=6.16(10)meV, x:=J_2/J_1=0.603(3), J_\perp=1.3(2)meV. To our knowledge this is the first quantitative treatment of bound states in a true 2d model.Comment: 4 pages, 3 figures, Proceeding paper of the HFM2000 conference in Waterloo, Canada, Jun 200

Dislocation-induced spin tunneling in Mn-12 acetate

Comprehensive theory of quantum spin relaxation in Mn-12 acetate crystals is developed, that takes into account imperfections of the crystal structure and is based upon the generalization of the Landau-Zener effect for incoherent tunneling from excited energy levels. It is shown that linear dislocations at plausible concentrations provide the transverse anisotropy which is the main source of tunneling in Mn-12. Local rotations of the easy axis due to dislocations result in a transverse magnetic field generated by the field applied along the c-axis of the crystal, which explains the presence of odd tunneling resonances. Long-range deformations due to dislocations produce a broad distribution of tunnel splittings. The theory predicts that at subkelvin temperatures the relaxation curves for different tunneling resonances can be scaled onto a single master curve. The magnetic relaxation in the thermally activated regime follows the stretched-exponential law with the exponent depending on the field, temperature, and concentration of defects.Comment: 17 pages, 14 figures, 1 table, submitted to PR

Tunneling with dissipation and decoherence for a large spin

We present rigorous solution of problems of tunneling with dissipation and decoherence for a spin of an atom or a molecule in an isotropic solid matrix. Our approach is based upon switching to a rotating coordinate system coupled to the local crystal field. We show that the spin of a molecule can be used in a qubit only if the molecule is strongly coupled with its atomic environment. This condition is a consequence of the conservation of the total angular momentum (spin + matrix), that has been largely ignored in previous studies of spin tunneling.Comment: 4 page

The three-dimensional random field Ising magnet: interfaces, scaling, and the nature of states

The nature of the zero temperature ordering transition in the 3D Gaussian random field Ising magnet is studied numerically, aided by scaling analyses. In the ferromagnetic phase the scaling of the roughness of the domain walls, $w\sim L^\zeta$, is consistent with the theoretical prediction $\zeta = 2/3$. As the randomness is increased through the transition, the probability distribution of the interfacial tension of domain walls scales as for a single second order transition. At the critical point, the fractal dimensions of domain walls and the fractal dimension of the outer surface of spin clusters are investigated: there are at least two distinct physically important fractal dimensions. These dimensions are argued to be related to combinations of the energy scaling exponent, $\theta$, which determines the violation of hyperscaling, the correlation length exponent $\nu$, and the magnetization exponent $\beta$. The value $\beta = 0.017\pm 0.005$ is derived from the magnetization: this estimate is supported by the study of the spin cluster size distribution at criticality. The variation of configurations in the interior of a sample with boundary conditions is consistent with the hypothesis that there is a single transition separating the disordered phase with one ground state from the ordered phase with two ground states. The array of results are shown to be consistent with a scaling picture and a geometric description of the influence of boundary conditions on the spins. The details of the algorithm used and its implementation are also described.Comment: 32 pp., 2 columns, 32 figure

On the Exact Evaluation of Certain Instances of the Potts Partition Function by Quantum Computers

We present an efficient quantum algorithm for the exact evaluation of either the fully ferromagnetic or anti-ferromagnetic q-state Potts partition function Z for a family of graphs related to irreducible cyclic codes. This problem is related to the evaluation of the Jones and Tutte polynomials. We consider the connection between the weight enumerator polynomial from coding theory and Z and exploit the fact that there exists a quantum algorithm for efficiently estimating Gauss sums in order to obtain the weight enumerator for a certain class of linear codes. In this way we demonstrate that for a certain class of sparse graphs, which we call Irreducible Cyclic Cocycle Code (ICCC_\epsilon) graphs, quantum computers provide a polynomial speed up in the difference between the number of edges and vertices of the graph, and an exponential speed up in q, over the best classical algorithms known to date

A Sawtooth-like Timeline for the First Billion Year of Lunar Bombardment

We revisit the early evolution of the Moon's bombardment. Our work combines modeling (based on plausible projectile sources and their dynamical decay rates) with constraints from the lunar crater record, radiometric ages of the youngest lunar basins, and the abundance of highly siderophile elements in the lunar crust and mantle. We deduce that the evolution of the impact flux did not decline exponentially over the first billion years of lunar history, but also there was no prominent and "narrow" impact spike some 3.9 Gy ago, unlike that typically envisioned in the lunar cataclysm scenario. Instead, we show the timeline of the lunar bombardment has a sawtooth-like profile, with an uptick in the impact flux near 4.1 Gy ago. The impact flux at the beginning of this weaker cataclysm was 5-10 times higher than the immediately preceding period. The Nectaris basin should have been one of the first basins formed at the sawtooth. We predict the bombardment rate since about 4.1Gy ago declined slowly and adhered relatively close to classic crater chronology models (Neukum and Ivanov (1994)). Overall we expect that the sawtooth event accounted for about 1/4 of the total bombardment suffered by the Moon since its formation. Consequently, considering that about 12-14 basins formed during the sawtooth event, we expect that the net number of basins formed on the Moon was about 45-50. From our expected bombardment timeline, we derived a new and improved lunar chronology suitable for use on Pre-Nectarian surface units. According to this chronology, a significant portion of the oldest lunar cratered terrains has an age of 4.38-4.42 Gyr. Moreover, the largest lunar basin, South Pole Aitken, is older than 4.3Gy, and therefore was not produced during the lunar cataclysm.Comment: In press in EPS

Spin Glasses on Thin Graphs

In a recent paper we found strong evidence from simulations that the Isingantiferromagnet on ``thin'' random graphs - Feynman diagrams - displayed amean-field spin glass transition. The intrinsic interest of considering such random graphs is that they give mean field results without long range interactions or the drawbacks, arising from boundary problems, of the Bethe lattice. In this paper we reprise the saddle point calculations for the Ising and Potts ferromagnet, antiferromagnet and spin glass on Feynman diagrams. We use standard results from bifurcation theory that enable us to treat an arbitrary number of replicas and any quenched bond distribution. We note the agreement between the ferromagnetic and spin glass transition temperatures thus calculated and those derived by analogy with the Bethe lattice, or in previous replica calculations. We then investigate numerically spin glasses with a plus or minus J bond distribution for the Ising and Q=3,4,10,50 state Potts models, paying particular attention to the independence of the spin glass transition from the fraction of positive and negative bonds in the Ising case and the qualitative form of the overlap distribution in all the models. The parallels with infinite range spin glass models in both the analytical calculations and simulations are pointed out.Comment: 13 pages of LaTex and 11 postscript figures bundled together with uufiles. Discussion of first order transitions for three or more replicas included and similarity to Ising replica magnet pointed out. Some additional reference

Crystal and magnetic structure of LaTiO3 : evidence for non-degenerate t2gt_{2g}-orbitals

The crystal and magnetic structure of LaTiO3 ~ has been studied by x-ray and neutron diffraction techniques using nearly stoichiometric samples. We find a strong structural anomaly near the antiferromagnetic ordering, T$_N$=146 K. In addition, the octahedra in LaTiO3 exhibit an intrinsic distortion which implies a splitting of the t2g-levels. Our results indicate that LaTiO3 should be considered as a Jahn-Teller system where the structural distortion and the resulting level splitting are enhanced by the magnetic ordering.Comment: 4 pages 5 figure