Random Spin Configurations Research Articles

Monte Carlo study of the phase diagram of layered XY antiferromagnet

The three-dimensional XY model is investigated in the presence of a uniform magnetic field applied in the X-direction. The nearest neighbour intraplanar interaction is considered ferromagnetic, and the interplanar nearest neighbour interaction is chosen to be antiferromagnetic. Starting from a high-temperature initial random spin configuration, the equilibrium phase of the system at any finite temperature was achieved by cooling the system using the Monte Carlo single spin-flip Metropolis algorithm with a random updating rule. The components of total magnetization and the sublattice magnetizations were calculated. The variance of the antiferromagnetic order parameter and the susceptibility have been calculated. In a specific range of relative strengths of interactions (antiferromagnetic/ferromagnetic) and the applied magnetic field, the system shows the equilibrium phase transitions at different temperatures. The phase diagrams (in the field-temperature plane) were obtained for different values of the relative interaction strengths. The ordered region bounded by the phase boundary was found to increase as the ratio of relative interaction strength increased. Furthermore, the maximum value of the susceptibility (χaym) was found to increase with the system size (L). For χaym∼Lγν, the exponent γ/ν has been estimated to be 2.10 ±0.11.

Diffuse optical tomography by simulated annealing via a spin Hamiltonian.

Diffuse optical tomography (DOT) is an imaging modality that uses near-infrared light. Although iterative numerical schemes are commonly used for its inverse problem, correct solutions are not obtained unless good initial guesses are chosen. We propose a numerical scheme of DOT, which works even when good initial guesses of optical parameters are not available. We use simulated annealing (SA), which is a method of the Markov-chain Monte Carlo. To implement SA for DOT, a spin Hamiltonian is introduced in the cost function, and the Metropolis algorithm or single-component Metropolis-Hastings algorithm is used. By numerical experiments, it is shown that an initial random spin configuration is brought to a converged configuration by SA, and targets in the medium are reconstructed. The proposed numerical method solves the inverse problem for DOT by finding the ground state of a spin Hamiltonian with SA.

Role of spin-glass behavior in the formation of exotic magnetic states in GdB6

Randomness and frustration are believed to be two crucial criteria for the formation of spin glass state. However, the spin freezing occurs in some well-ordered crystals below the related temperature Tf due to the instability of each spin state, which induces the variation of either magnetic moment value or exchange energy. Here we explore the new mechanism of the in-site originated disorder in antiferromagnets Gd0.73La0.27B6 and GdB6, which is caused by the random mutual shifts of Gd3+ spins from the centrally symmetrical positions in the regular cubic lattice. The universal scaling of ESR linewidth temperature dependencies to the power law ΔH(T) ~ ((T − TD)/TD)α with α = − 1.1 ± 0.05 in the paramagnetic phase of both compounds demonstrates the identity of the origin of magnetic randomness. In Gd0.73La0.27B6 the resulting random spin configurations freeze at Tf ≈ 10.5 K where the maximum of magnetization is observed. Below Tf the splitting of ZFC and FC magnetization curves takes place as well as the magnetic state depends on the antecedent sample history. In the case of GdB6 the coherent displacement of Gd ions compete with these random shifts forming an antiferromagnetic (AFM) phase at TN = 15.5 K, which prevails over the spin freezing at Tf ≈ 13 K, expected from the ESR data. The observation of the hysteresis of the ESR spectrum in the AFM phase suggests that its properties may be determined by the competition of two types of AFM orders, which results in formation of stable magnetic domains with nonequivalent positions of AFM Gd pairs at T < 10 K.

Exploration of antiferromagnetic CoO and NiO using reverse Monte Carlo total neutron scattering refinements

The atomic and magnetic structures of CoO and NiO have been probed using reverse Monte Carlo (RMC) refinements of neutron total scattering data. The results obtained show that the known magnetic structure for NiO can be recovered by the RMC process starting from random spin configurations, but it is insensitive to the spin direction in the {111} ferromagnetic planes. Refinements of the magnetic structure of CoO starting from random spin configurations result in collinear or non-collinear magnetic structures, consistent with those reported by other techniques. Starting from an ordered collinear spin structure for CoO and NiO leads to different results than when starting from a random arrangement of spins, which is evidence for configurational bias that highlights the need to take care when selecting a starting model for RMC refinements of magnetic structures.

Height representation of XOR-Ising loops via bipartite dimers

The XOR-Ising model on a graph consists of random spin configurations on vertices of the graph obtained by taking the product at each vertex of the spins of two independent Ising models. In this paper, we explicitly relate loop configurations of the XOR-Ising model and those of a dimer model living on a decorated, bipartite version of the Ising graph. This result is proved for graphs embedded in compact surfaces of genus $g$. Using this fact, we then prove that XOR-Ising loops have the same law as level lines of the height function of this bipartite dimer model. At criticality, the height function is known to converge weakly in distribution to $\frac{1}{\sqrt{\pi}}$ a Gaussian free field. As a consequence, results of this paper shed a light on the occurrence of the Gaussian free field in the XOR-Ising model. In particular, they provide a step forward in the solution of Wilson's conjecture, stating that the scaling limit of XOR-Ising loops are level lines of the Gaussian free field.

Random spin configurations of Co cations in LaCo 1− xMg xO 3 (0 < x ≤ 0.20) perovskite oxides: Magnetic and transport properties

Perovskite-type cobaltites LaCo 1− x Mg x O 3 (0 < x ≤ 0.20) were synthesised by the liquid mix technique and structurally characterised by X-ray diffraction and neutron powder diffraction. This system can be regarded as LaCoO 3-derived by means of partial substitution of trivalent cobalt ions by Mg 2+. This doping is accompanied by the stabilization of the correspondent amount of Co 4+ cations as it has been established from ICP, thermogravimetric and neutron diffraction results. The title materials behave as semiconductors up to 800 K. Above this temperature they show a transition to the metallic state. Magnetic susceptibility and magnetization measurements show weak ferromagnetic interactions at 5 K which has been interpreted taking into account disordered spin configurations for the cobalt cations.

Mechanism for the failure of the Edwards hypothesis in the Sherrington-Kirkpatrick spin glass

The dynamics of the Sherrington-Kirkpatrick model at $T=0$ starting from random spin configurations is considered. The metastable states reached by such dynamics are atypical of such states as a whole, in that the probability density of site energies, $p(\ensuremath{\lambda})$, is small at $\ensuremath{\lambda}=0$. Since virtually all metastable states have a much larger $p(0)$, this behavior demonstrates a qualitative failure of the Edwards hypothesis. We look for its origins by modeling the changes in the site energies during the dynamics as a Markov process. We show how the small $p(0)$ arises from features of the Markov process that have a clear physical basis in the spin glass, and hence explain the failure of the Edwards hypothesis.

A new study on the doped Mott-Hubbard insulator

By introducing a rotationally invariant Stratonovich–Hubbard (S-H) field we studied the doped Mott insulator phase of the two-dimension Hubbard model for U/t∼4–8. The static spin is decoupled by the S–H field and the static charge interaction is then treated by Hartree–Fock approximation. We sample random spin configurations by Monte Carlo simulation with the Metropolis updating algorithm. The Mott–Hubbard gap and static susceptibilities are studied near the half-filling at low temperature.

Density of hole states for the strongly correlated infinite-dimensional Hubbard model.

The density of hole states for the strongly correlated infinite-dimensional Hubbard model is studied with use of the moment-expansion method. While exact results suggest a divergent spectrum width for ferromagnetic spin configurations, numerical calculations indicate a finite spectrum width for antiferromagnetic and random spin configurations. The spectrum widths for antiferromagnetic and random spin configurations are 5.6568\ifmmode\pm\else\textpm\fi{}0.0001 and 10\ifmmode\pm\else\textpm\fi{}2, respectively.

Spin-fluctuation statistics in CuMn.

The resistance of small ${\mathrm{Cu}}_{0.91}$${\mathrm{Mn}}_{0.09}$ samples in the spin-glass phase showed random changes upon thermal cycling, quantitatively showing that random spin configurations affect universal conductance fluctuations. Low-frequency resistance noise showed large non-Gaussian effects, which were inconsistent with the simplest droplet models for spin glasses. A typical spin-rearrangement event involved about ${10}^{4}$ spins. Several detailed statistical parameters were measured for comparison with droplet and hierarchical models.

Ten-fold degenerate d-electron correlation and the metal-nonmetal transition in a disordered binary system: Inclusion of Hund's rule coupling

The Yonezawa-Watabe (YW) study of the metal-nonmetal transitions in nondegenerate, s-electron disordered binary systems: doped semiconductors, metal-ammonia solutions, liquid metals and mixed crystals (alloys), is generalized to include ten-fold d-electron (hole) degeneracy. Such degeneracy automatically includes Hund's rule d-electron coupling and intra-site enhanced Coulomb and exchange interactions. Such a calculation is specifically relevant only to transition metal alloys, transition metal oxides and mixed transition metal oxides. It is seen that potential fluctuations exist in these systems and the possibility of Anderson localization in these disordered degenerate binary transition metal systems is explored. The YW CPA treatment of the effect of substitutional disorder (alloying) upon the mobility gap and quasiparticle states of the density of states at the extreme band edges and localization due to random spin configuration are generalized to these degenerate d-electron systems and it is shown that the disappearance of the mobility gap, not the density of states gap, causes the metal-nonmetal transition for degenerate d-electrons.