Fast spin dynamics algorithms for classical spin systems

We have proposed new algorithms for the numerical integration of the equations of motion for classical spin systems. In close analogy to symplectic integrators for Hamiltonian equations of motion used in Molecular Dynamics these algorithms are based on the Suzuki-Trotter decomposition of exponential operators and unlike more commonly used algorithms exactly conserve spin length and, in special cases, energy. Using higher order decompositions we investigate integration schemes of up to fourth order and compare them to a well established fourth order predictor-corrector method. We demonstrate that these methods can be used with much larger time steps than the predictor-corrector method and thus may lead to a substantial speedup of computer simulations of the dynamical behavior of magnetic materials.Comment: 9 pages RevTeX with 8 figure

Percolation in three-dimensional random field Ising magnets

The structure of the three-dimensional random field Ising magnet is studied by ground state calculations. We investigate the percolation of the minority spin orientation in the paramagnetic phase above the bulk phase transition, located at [Delta/J]_c ~= 2.27, where Delta is the standard deviation of the Gaussian random fields (J=1). With an external field H there is a disorder strength dependent critical field +/- H_c(Delta) for the down (or up) spin spanning. The percolation transition is in the standard percolation universality class. H_c ~ (Delta - Delta_p)^{delta}, where Delta_p = 2.43 +/- 0.01 and delta = 1.31 +/- 0.03, implying a critical line for Delta_c < Delta <= Delta_p. When, with zero external field, Delta is decreased from a large value there is a transition from the simultaneous up and down spin spanning, with probability Pi_{uparrow downarrow} = 1.00 to Pi_{uparrow downarrow} = 0. This is located at Delta = 2.32 +/- 0.01, i.e., above Delta_c. The spanning cluster has the fractal dimension of standard percolation D_f = 2.53 at H = H_c(Delta). We provide evidence that this is asymptotically true even at H=0 for Delta_c < Delta <= Delta_p beyond a crossover scale that diverges as Delta_c is approached from above. Percolation implies extra finite size effects in the ground states of the 3D RFIM.Comment: replaced with version to appear in Physical Review

Considerations on the quantum double-exchange Hamiltonian

Schwinger bosons allow for an advantageous representation of quantum double-exchange. We review this subject, comment on previous results, and address the transition to the semiclassical limit. We derive an effective fermionic Hamiltonian for the spin-dependent hopping of holes interacting with a background of local spins, which is used in a related publication within a two-phase description of colossal magnetoresistant manganites.Comment: 7 pages, 3 figure

The hyperfine transition in light muonic atoms of odd Z

The hyperfine (hf) transition rates for muonic atoms have been re-measured for select light nuclei, using neutron detectors to evaluate the time dependence of muon capture. For $^{19}$F $\Lambda$$_{h}$ = 5.6 (2) $\mu$s$^{-1}$ for the hf transition rate, a value which is considerably more accurate than previous measurements. Results are also reported for Na, Al, P, Cl, and K; that result for P is the first positive identification.Comment: 12 pages including 5 tables and 4 figures, RevTex, submitted to Phys. Rev.

Revisiting the scaling of the specific heat of the three-dimensional random-field Ising model

We revisit the scaling behavior of the specific heat of the three-dimensional random-field Ising model with a Gaussian distribution of the disorder. Exact ground states of the model are obtained using graph-theoretical algorithms for different strengths = 268 3 spins. By numerically differentiating the bond energy with respect to h, a specific-heat-like quantity is obtained whose maximum is found to converge to a constant in the thermodynamic limit. Compared to a previous study following the same approach, we have studied here much larger system sizes with an increased statistical accuracy. We discuss the relevance of our results under the prism of a modified Rushbrooke inequality for the case of a saturating specific heat. Finally, as a byproduct of our analysis, we provide high-accuracy estimates of the critical field hc = 2.279(7) and the critical exponent of the correlation exponent ν = 1.37(1), in excellent agreement to the most recent computations in the literature

Effects of Pore Walls and Randomness on Phase Transitions in Porous Media

We study spin models within the mean field approximation to elucidate the topology of the phase diagrams of systems modeling the liquid-vapor transition and the separation of He$^3$--He$^4$ mixtures in periodic porous media. These topologies are found to be identical to those of the corresponding random field and random anisotropy spin systems with a bimodal distribution of the randomness. Our results suggest that the presence of walls (periodic or otherwise) are a key factor determining the nature of the phase diagram in porous media.Comment: REVTeX, 11 eps figures, to appear in Phys. Rev.

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

Frustration and the Kondo effect in heavy fermion materials

The observation of a separation between the antiferromagnetic phase boundary and the small-large Fermi surface transition in recent experiments has led to the proposal that frustration is an important additional tuning parameter in the Kondo lattice model of heavy fermion materials. The introduction of a Kondo (K) and a frustration (Q) axis into the phase diagram permits us to discuss the physics of heavy fermion materials in a broader perspective. The current experimental situation is analysed in the context of this combined "QK" phase diagram. We discuss various theoretical models for the frustrated Kondo lattice, using general arguments to characterize the nature of the $f$-electron localization transition that occurs between the spin liquid and heavy Fermi liquid ground-states. We concentrate in particular on the Shastry--Sutherland Kondo lattice model, for which we establish the qualitative phase diagram using strong coupling arguments and the large-$N$ expansion. The paper closes with some brief remarks on promising future theoretical directions.Comment: To appear in a special issue of JLT

Critical aspects of the random-field Ising model

We investigate the critical behavior of the three-dimensional random-field Ising model (RFIM) with a Gaussian field distribution at zero temperature. By implementing a computational approach that maps the ground-state of the RFIM to the maximum-flow optimization problem of a network, we simulate large ensembles of disorder realizations of the model for a broad range of values of the disorder strength h and system sizes  = L3, with L ≤ 156. Our averaging procedure outcomes previous studies of the model, increasing the sampling of ground states by a factor of 103. Using well-established finite-size scaling schemes, the fourth-order’s Binder cumulant, and the sample-to-sample fluctuations of various thermodynamic quantities, we provide high-accuracy estimates for the critical field hc, as well as the critical exponents ν, β/ν, and γ̅/ν of the correlation length, order parameter, and disconnected susceptibility, respectively. Moreover, using properly defined noise to signal ratios, we depict the variation of the self-averaging property of the model, by crossing the phase boundary into the ordered phase. Finally, we discuss the controversial issue of the specific heat based on a scaling analysis of the bond energy, providing evidence that its critical exponent α ≈ 0−

Energy and system size dependence of \phi meson production in Cu+Cu and Au+Au collisions

We study the beam-energy and system-size dependence of \phi meson production (using the hadronic decay mode \phi -- K+K-) by comparing the new results from Cu+Cu collisions and previously reported Au+Au collisions at \sqrt{s_NN} = 62.4 and 200 GeV measured in the STAR experiment at RHIC. Data presented are from mid-rapidity (|y|<0.5) for 0.4 < pT < 5 GeV/c. At a given beam energy, the transverse momentum distributions for \phi mesons are observed to be similar in yield and shape for Cu+Cu and Au+Au colliding systems with similar average numbers of participating nucleons. The \phi meson yields in nucleus-nucleus collisions, normalised by the average number of participating nucleons, are found to be enhanced relative to those from p+p collisions with a different trend compared to strange baryons. The enhancement for \phi mesons is observed to be higher at \sqrt{s_NN} = 200 GeV compared to 62.4 GeV. These observations for the produced \phi(s\bar{s}) mesons clearly suggest that, at these collision energies, the source of enhancement of strange hadrons is related to the formation of a dense partonic medium in high energy nucleus-nucleus collisions and cannot be alone due to canonical suppression of their production in smaller systems.Comment: 20 pages and 5 figure