Microscopic Spin Model Research Articles

Bulk magnetoelectricity in the hexagonal manganites and ferrites

Improper ferroelectricity (trimerization) in the hexagonal manganites RMnO3 leads to a network of coupled structural and magnetic vortices that induce domain wall magnetoelectricity and magnetization (M), neither of which, however, occurs in the bulk. Here we combine first-principles calculations, group-theoretic techniques and microscopic spin models to show how the trimerization not only induces a polarization (P) but also a bulk M and bulk magnetoelectric (ME) effect. This results in the existence of a bulk linear ME vortex structure or a bulk ME coupling such that if P reverses so does M. To measure the predicted ME vortex, we suggest RMnO3 under large magnetic field. We suggest a family of materials, the hexagonal RFeO3 ferrites, also display the predicted phenomena in their ground state.

Disconnected glass-glass transitions and swallowtail bifurcations in microscopic spin models with facilitated dynamics

It has been recently established that heterogeneous bootstrap percolation and related dynamic facilitation models exhibit a complex hierarchy of continuous and discontinuous transitions depending on lattice connectivity and kinetic constraints. Here the range of the previously observed phase diagram topologies and higher-order singularities is extended to disconnected glass-glass transitions and to cusp and swallowtail bifurcations (which can be generic and degenerate). The phase diagram and the order parameter for two different types of spin mixtures are analytically determined and an experimental realization of the new predictions emerging in our approach is suggested.

Finite-size critical fluctuations in microscopic models of mode-coupling theory

Facilitated spin models on random graphs provide an ideal microscopic realization of the mode-coupling theory of supercooled liquids: they undergo a purely dynamic glass transition with no thermodynamic singularity. In this paper we study the fluctuations of dynamical heterogeneity and their finite-size scaling properties in the β relaxation regime of such microscopic spin models. We compare the critical fluctuation behavior for two distinct measures of correlations with the results of a recently proposed field theoretical description based on quasi-equilibrium ideas. We find that the theoretical predictions perfectly fit the numerical simulation data once the relevant order parameter is identified with the persistence function of the spins.

Universal finite-temperature properties of a three-dimensional quantum antiferromagnet in the vicinity of a quantum critical point

We consider a 3-dimensional quantum antiferromagnet which can be driven through a quantum critical point (QCP) by varying a tuning parameter g. Starting from the magnetically ordered phase, the N{\'e}el temperature will decrease to zero as the QCP is approached. From a generic quantum field theory, together with numerical results from a specific microscopic Heisenberg spin model, we demonstrate the existence of universal behaviour near the QCP. We compare our results with available data for TlCuCl_3

(3+1)-TQFTs and topological insulators

Levin-Wen models are microscopic spin models for topological phases of matter in (2+1)-dimension. We introduce a generalization of such models to (3 + 1)-dimension based on unitary braided fusion categories, also known as unitary premodular categories. We discuss the ground state degeneracy on 3-manifolds and statistics of excitations which include both points and defect loops. Potential connections with recently proposed fractional topological insulators and projective ribbon permutation statistics are described.

Multiferroic response to magnetic field in orthorhombic manganites

The magnetoelectric coupling in Eu0.55Y0.45MnO3 is studied based on a microscopic spin model which includes the superexchange interaction, the single-ion anisotropy, the Dzyaloshinskii–Moriya interaction, and the cubic anisotropy. Our Monte Carlo simulation reproduces the experimentally observed multiferroic response to magnetic field B. It is demonstrated that the magnetic field can control the multiferroic behaviors by modulating the spin arrangements, leading to various flops of electric polarization. In addition, an interesting state in which both the electric polarizations along the a-axis and c-axis are activated under high B is predicted and discussed.

Microscopic formulation of the Zimm-Bragg model for the helix-coil transition

A microscopic spin model is proposed for the phenomenological Zimm-Bragg model for the helix-coil transition in biopolymers. This model is shown to provide the same thermophysical properties of the original Zimm-Bragg model and it allows a very convenient framework to compute statistical quantities. Physical origins of this spin model are made transparent by an exact mapping into a one-dimensional Ising model with an external field. However, the dependence on temperature of the reduced external field turns out to differ from the standard one-dimensional Ising model and hence it gives rise to different thermophysical properties, despite the exact mapping connecting them. We discuss how this point has been frequently overlooked in the recent literature.

Microscopic model and phase diagrams of the multiferroic perovskite manganites

Orthorhombically distorted perovskite manganites, $R\mathrm{Mn}{\mathrm{O}}_{3}$ with $R$ being a trivalent rare-earth ion, exhibit a variety of magnetic and electric phases including multiferroic (i.e., concurrently magnetic and ferroelectric) phases and fascinating magnetoelectric phenomena. We theoretically study the phase diagram of $R\mathrm{Mn}{\mathrm{O}}_{3}$ by constructing a microscopic spin model, which includes not only the superexchange interaction but also the single-ion anisotropy (SIA) and the Dzyaloshinsky-Moriya interaction (DMI). Analysis of this model using the Monte Carlo method reproduces the experimental phase diagrams as functions of the $R$-ion radius, which contain two different multiferroic states, i.e., the $ab$-plane spin cycloid with ferroelectric polarization $P\ensuremath{\parallel}a$ and the $bc$-plane spin cycloid with $P\ensuremath{\parallel}c$. The orthorhombic lattice distortion or the second-neighbor spin exchanges enhanced by this distortion exquisitely controls the keen competition between these two phases through tuning the SIA and DMI energies. This leads to a lattice-distortion-induced reorientation of $P$ from $a$ to $c$ in agreement with the experiments. We also discuss spin structures in the $A$-type antiferromagnetic state, those in the cycloidal spin states, origin and nature of the sinusoidal collinear spin state, and many other issues.

Microscopic spin model for the stock market with attractor bubbling on scale-free networks

A multi-agent spin model for changes of prices in the stock market based on the Ising-like cellular automaton with interactions between traders randomly varying in time is investigated by means of Monte Carlo simulations. The structure of interactions has topology of scale-free networks with degree distributions obeying a power scaling law with various scaling exponents. The scale-free networks are obtained as growing networks where new nodes (agents) are linked to the existing ones according to a preferential attachment rule with an initial attractiveness ascribed to each node. In certain ranges of parameters, depending on the exponent in the degree distribution, the time series of the logarithmic price returns exhibit intermittent bursting typical of volatility clustering, and the tails of the distributions of returns obey a power scaling law with exponents comparable to those obtained from the empirical data. The distributions of returns show also dependence on the number of agents, in particular in the case of networks with the scaling exponents of the degree distributions typical of the social and communications networks.

Spin-Peierls instabilities of antiferromagnetic rings in a magnetic field

Motivated by the intriguing properties of magnetic molecular wheels at field-induced level crossings, we investigate the spin-Peierls instability of antiferromagnetic rings in a field by exact diagonalizations of a microscopic spin model coupled to the lattice via a distortion-dependent Dzyaloshinskii-Moriya interaction. We show that, beyond the unconditional instability at level crossings for infinitesimal magnetoelastic coupling, the model is characterized by a stronger tendency to distort at higher level crossings and by a dramatic angular dependence with very sharp torque anomalies when the field is almost in the plane of the ring. These predictions are shown to compare remarkably well with available torque and nuclear magnetic resonance data on CsFe8.

Increasing market efficiency in the stock markets

We study the temporal evolutions of three stock markets; Standard and Poor's 500 index, Nikkei 225 Stock Average, and the Korea Composite Stock Price Index. We observe that the probability density function of the log-return has a fat tail but the tail index has been increasing continuously in recent years. We have also found that the variance of the autocorrelation function, the scaling exponent of the standard deviation, and the statistical complexity decrease, but that the entropy density increases as time goes over time. We introduce a modified microscopic spin model and simulate the model to confirm such increasing and decreasing tendencies in statistical quantities. These findings indicate that these three stock markets are becoming more efficient.

Increasing market efficiency in the stock markets

We study the temporal evolutions of three stock markets; Standard and Poor's 500 index, Nikkei 225 Stock Average, and the Korea Composite Stock Price Index. We observe that the probability density function of the log-return has a fat tail but the tail index has been increasing continuously in recent years. We have also found that the variance of the autocorrelation function, the scaling exponent of the standard deviation, and the statistical complexity decrease, but that the entropy density increases as time goes over time. We introduce a modified microscopic spin model and simulate the model to confirm such increasing and decreasing tendencies in statistical quantities. These findings indicate that these three stock markets are becoming more efficient.

Microscopic spin model for the dynamics of the return distribution of the Korean stock market index

In this paper, we studied the dynamics of the log-return distribution of the Korean Composition Stock Price Index (KOSPI) from 1992 to 2004. Based on the microscopic spin model, we found that while the index during the late 1990s showed a power-law distribution, the distribution in the early 2000s was exponential. This change in distribution shape was caused by the duration and velocity, among other parameters, of the information that flowed into the market.

Time dependence of muon spin relaxation spectra and spin correlation functions

The existing theory of the microscopic interpretation of the dynamical contribution to zero-field muon depolarization spectra in a longitudinal geometry is developed. The predicted relaxation of the muon depolarization is calculated from two forms of the spin correlation function. First, when the spin correlation function has an exponential form with a single wave-vector-dependent relaxation rate considered, it is shown that this form of the spin correlation function reproduces the slow and fast fluctuation limits of stochastic spin theory regardless of the choice of microscopic spin model. Second, if the spin correlation function is a homogeneous scaling function (such as a power-law decay with time), as suggested by the mode-coupling theory of spin dynamics, this results in a stretched exponential relaxation of the muon spectra. For simple spin diffusion, the muon spectra are shown to be relaxed with a root-exponential form.

Large-scale simulations of the finite-temperature properties of the molecular assemblies Mn6 and Ni12

The numerical transfer-matrix approach and the exact diagonalization technique are worked out for the isotropic Heisenberg model with the uniform and alternating spin variables within the ring geometry. They are applied in large-scale simulations to the above cyclic organometallic clusters Mn6 (i.e. [Mn(hfac)2NITPh]6) and Ni12 (i.e. Ni12(O2CMe)12(chp)12(H2O)6(THF)6) in order to quantitatively model their magnetic properties. For the Ni12 complex new experimental data are also reported. The microscopic spin model parameters for both molecules are obtained from a fit of the theoretical curves to the experimental results.

Finite-temperature characterization and simulations of the molecular assemblies Mn 6 and Ni 12

Numerical transfer-matrix approach and exact diagonalization technique exploiting the point-group symmetry and the properties of the shift operator are worked out in the framework of quantum statistical mechanics for the isotropic Heisenberg spin Hamiltonian with the ring geometry. They are applied in large-scale simulations to the title high nuclearity cyclic clusters Mn6 (i.e. [Mn(hfac)2NITPh]6) and Ni12 (i.e. Ni12(O2CMe)12(chp)12(H2O)6(THF)6) in order to model quantitatively their magnetic properties. For Ni12 complex new experimental susceptibility data are also reported. New microscopic spin model parameters for both molecules are obtained from a fit of the theoretical susceptibility curves to the experimental results.

Symmetries in magnetic phase transitions: I. The Landau-Ginzburg-Wilson Hamiltonian

The Landau-Ginzburg-Wilson Hamiltonian is a function that relates Landau's phenomenological theory of magnetic phase transitions to the quantum mechanics of a microscopic spin model. The authors study how the symmetry of the system under consideration manifests itself in these different descriptions of the thermodynamic properties (density operator, LGW Hamiltonian, other functions of the order parameters). The results of this discussion are used to comment on divergent opinions in the literature concerning the use of corepresentations in magnetic phase transitions.

Magnetic field induced spin reorientation transitions in U 3Sb 4

Magnetisation curves along the 〈111〉 and 〈100〉 axes have been measured for U 3Sb 4 at temperatures between 4.2 and 180 K and in fields up to 6 T. The temperature variation of the critical field as well as the value of the magnetisation jump observed at the spin reorientation induced by the field along the 〈111〉 axis, have been determined. The results are discussed in the framework of a microscopic spin model which takes into account both anisotropic crystal field and anisotropic exchange interactions.

High field magnetisation and hall effect of U 3Sb 4 single crystals

We have examined the Hall effect of U 3Sb 4 (T c = 146 K) in the paramagnetic and ferromagnetic ranges as well as the magnetisation along three principal directions at 4.2 K and in fields up to 35 T. Both ordinary and extraordinary Hall constants are positive, giving the hole concentration of 1.2 × 10 20 cm −3. The easy magnetic axis was found to be 〈100〉, and the uranium moment was determined to be 2μ B. Magnetisation jumps at 4.9 and 17.6 T in fields along the 〈111〈 and 〈110〉 direction, respectively, were also found. A microscopic spin model including crystal-field and anisotropic-exchange interactions predicts magnetisation behaviour in qualitative agreement with that observed experimentally for U 3X 4 (X = P, As, Sb) compounds, and it shows that the observed jumps are spin-orientational transitions.

Discontinuous Phase Transitions Induced by Magnetic Field in a Ferromagnet such as U3X4. Application to U3As4

AbstractIn the framework of a microscopic spin model which contains the fourth‐order crystal‐field anisotropy terms it is shown that the first‐order phase transitions induced by magnetic field are possible in ferromagnets such as U3X4. Using the variational method the behaviour of the system in external fields of various orientations at zero temperature is discussed. The critical field as a function of Hamiltonian parameters and the tricritical point line are found. The dependence of the magnetization on the magnetic field value is also determined. The results obtained are qualitatively consistent with the experimental data for U3As4.