Four-spin Interaction Research Articles

Multicriticality of the three-dimensional Ising model with plaquette interactions: an extension of Novotny's transfer-matrix formalism.

A three-dimensional Ising model with the plaquette-type (next-nearest-neighbor and four-spin) interactions is investigated numerically. This extended Ising model, the so-called gonihedric model, was introduced by Savvidy and Wegner as a discretized version of the interacting (closed) surfaces without surface tension. The gonihedric model is notorious for its slow relaxation to the thermal equilibrium (glassy behavior), which deteriorates the efficiency of the Monte Carlo sampling. We employ the transfer-matrix (TM) method, implementing Novotny's idea, which enables us to treat an arbitrary number of spins N for one TM slice even in three dimensions. This arbitrariness admits systematic finite-size-scaling analyses. Accepting the extended parameter space by Cirillo et al., we analyzed the (multi-) criticality of the gonihedric model for N</=13. Thereby, we found that, as first noted by Cirillo et al. analytically (cluster-variation method), the data are well described by the multicritical (crossover) scaling theory. That is, the previously reported nonstandard criticality for the gonihedric model is reconciled with a crossover exponent and the ordinary three-dimensional-Ising universality class. We estimate the crossover exponent and the correlation-length critical exponent at the multicritical point as phi=0.6(2) and nu; =0.45(15), respectively.

Temperature effects on the dynamics of the 1-D transverse Ising model with four-spin interactions

The dynamics of one-dimensional quantum spin systems has been a long standing theoretical and experimental problem. Among them, the transverse Ising model with multi-spin interactions, regarded as one of the simplest with non-trivial dynamics, has attracted considerable interest in recent years. We investigate the temperature effects on the dynamics of the transverse Ising model with four-spin interactions. The model is relevant to the physics of poly(vinylidene fluoride-trifluoroethylene)[P(VDF-TrFE)] copolymers. We determine the time-dependent correlation function and spectral density for all temperatures for cases where the transverse field B is less, equal or greater than the four-spin coupling J. Our calculations were done with rings of up to 11 spins. However the results presented are also valid in the thermodynamic limit. We find that the time-dependent correlation function in general has oscillatory behavior when the transverse field is stronger than the coupling energy. On the other hand, when the field is weaker the real part of the time-dependent correlation function decreases monotonically at high enough temperatures. The temperature effects are best seen from the spectral density: at zero temperature the system can only absorb energy and, as the temperature is raised, the correlation functions keep memory of the zero-temperature quantum phases. Such feature persists up to the infinite temperature limit.

Exact results of a mixed spin- [formula omitted] and spin-1 transverse Ising model with two- and four-spin interactions and crystal field on the honeycomb lattice

A mixed spin- 1 2 and spin-1 transverse Ising model with two- and four-spin interactions and crystal field on the honeycomb lattice is studied using a generalized mapping transformation technique. Exact expressions for the critical temperature, the magnetization, the correlation functions, the internal energy and other thermodynamic quantities are obtained. The phase diagram is obtained as a function of the interaction parameter, crystal field or the transverse field. It is found out that the system belongs to the Onsager universality class in some region of the four-spin interaction parameter space and to the Villain–Stephenson universality class in the other region. The detailed analysis reveals that the system with nonzero transverse field is ordered regardless of the value of the crystal field.

Monte Carlo simulation on Ising spin system with two-spin and four-spin interactions

The magnetization, the specific heat and the Curie temperature of the Ising spin system with two-spin and four-spin interactions have been investigated by making use of the Monte Carlo simulation. In low temperature region, the magnetization and the specific heat curves show different characteristic behaviors for the three-site four-spin interaction and the four-site four-spin interaction.

Thermodynamic properties of temperature graded ferroelectric film

Effects of quantum fluctuation and four-spin interaction on the polarizationand pyroelectric coefficient of temperature graded ferroelectric film areinvestigated, based on the transverse Ising model by taking into accountthe four-spin interaction. It is found that the magnitude and the signof the polarization gradient are dependent on the imposed temperaturegradient, and both the quantum fluctuation and four-spin interaction play animportant role in the thermodynamic properties of the temperature gradedfilm. With increasing strength of the quantum fluctuations the sharppeak of the pyroelectric coefficient shifts to lower temperatures. Also thefour-spin interaction increases the mean polarization and makes the smoothpyroelectric peak at low temperature more pronounced. Furthermore, the gradedferroelectric film shows the characteristic feature of a first-order phase transitionwhen the four-spin interaction is larger than a critical value, which isdependent on the temperature gradient and the quantum fluctuation.

Rung-singlet phase of theS=12two-leg spin-ladder with four-spin cyclic exchange

Using continuous unitary transformations (CUT) we calculate the one-triplet gap for the antiferromagnetic S=1/2 two-leg spin ladder with additional four-spin exchange interactions in a high order series expansion about the limit of isolated rungs. By applying a novel extrapolation technique we calculate the transition line between the rung-singlet phase and a spontaneously dimerized phase with dimers on the legs. Using this efficient extrapolation technique we are able to analyze the crossover from strong rung coupling to weakly coupled chains.

Optical absorption of S= two-leg spin ladder systems

Abstract We calculate the optical absorption spectrums for the S= 1 2 two-leg spin ladder systems using continued fraction method based on Lanczos algorithm. We use two sets of parameters suggested for an S= 1 2 two-leg spin ladder material SrCu2O3. We find that due to a cyclic four-spin interaction the dispersion curve becomes flatter and hence, the large peak structure appears in the optical absorption spectrums.

Optical absorption spectra inSrCu2O3two-leg spin ladder

We calculate the phonon-assisted optical-absorption spectra in ${\mathrm{SrCu}}_{2}{\mathrm{O}}_{3}$ two-leg spin-ladder systems. The results for two models proposed for ${\mathrm{SrCu}}_{2}{\mathrm{O}}_{3}$ are compared. In the model including the effects of a cyclic four-spin interaction, the shoulder structure appears at $\ensuremath{\sim}978{\mathrm{cm}}^{\ensuremath{-}1}$ and the peak appears at $\ensuremath{\sim}1975{\mathrm{cm}}^{\ensuremath{-}1}$ in the spectrum for polarization of the electric field parallel to the legs. In the other model which describes a pure two-leg ladder, the peak appears around the lower edge of the spectrum at $\ensuremath{\sim}1344{\mathrm{cm}}^{\ensuremath{-}1}.$ The feature can be effective in determining the proper model for ${\mathrm{SrCu}}_{2}{\mathrm{O}}_{3}.$

Exact results of a mixed spin- [formula omitted] and spin- S transverse Ising model with two- and four-spin interactions on the honeycomb lattice

A mixed spin- 1 2 and spin- S transverse Ising model with two- and four-spin interactions on the honeycomb lattice is studied using a generalized mapping transformation technique. The exact expressions for the critical temperature, the magnetization, the correlation functions, the internal energy and other thermodynamic quantities are obtained. The phase diagram is obtained as a function of the interaction parameter or the transverse field.

Magnetization and ground state spin structures of Ising spin system with four-spin interaction

The magnetization of spin S(= 1 2 and 1) Ising systems with bilinear and four-site four-spin interactions has been investigated by making use of the Monte Carlo simulation. In low-temperature region, the magnetization curves show an anomalous inverse inclination and decrease (increase) with the decrease (increase) of temperature within a certain exchange ratio range. The relation between the value of the magnetization at zero-temperature and the spin structure expected for the ground state is discussed.

The effects of a non-ferroelectric slab on the polarization and the susceptibility of a ferroelectric multilayer

The polarization and the susceptibility of ferroelectric multilayers with a non-ferroelectric slab are investigated within the framework of the transverse Ising model (TIM) with a four-spin interaction term. The effect of the thickness and the position of the non-ferroelectric slab are investigated in this paper. We find that the increase in the thickness of the non-ferroelectric slab will decrease the polarization and the susceptibility of the film. If the position of the non-ferroelectric slab shifts from the center of the film to the surface, the number of peaks in the susceptibility will change and a step-like polarization curve should be found.

Dynamical structure factors ofS=12two-leg spin-ladder systems

We investigate dynamical properties of $S=1/2$ two-leg spin ladder systems. In a strong coupling region, an isolated mode appears in the lowest excited states, while in a weak coupling region, an isolated mode is reduced and the lowest excited states become a lower bound of the excitation continuum. We find in the system with equal intrachain and interchain couplings that due to a cyclic four-spin interaction, the distribution of the weights for the dynamical structure factor and characteristics of the lowest excited states are strongly influenced. The dynamical properties of two systems proposed for ${\rm SrCu_2O_3}$ are also discussed.

Charge stripes based on higher-order interactions in cuprate superconductors

The origin of the charge stripe order in the high- T c cuprate superconductors is investigated based on the framework of the two-dimensional t– J model. We propose a mechanism of the stripe due to the higher-order corrections in the t– J model; the next-nearest-neighbor exchange interaction J ′ and/or the four-spin exchange interaction J 4. We also calculate some hole correlation functions of the finite cluster of the model using the numerical diagonalization, to examine the realization of the mechanism.

Fractionalization in an easy-axis Kagome antiferromagnet

We study an antiferromagnetic spin-1/2 model with up to third nearest-neighbor couplings on the Kagome lattice in the easy-axis limit, and show that its low-energy dynamics are governed by a four site XY ring exchange Hamiltonian. Simple ``vortex pairing'' arguments suggest that the model sustains a novel fractionalized phase, which we confirm by exactly solving a modification of the Hamiltonian including a further four-site interaction. In this limit, the system is a featureless ``spin liquid'', with gaps to all excitations, in particular: deconfined S^z=1/2 bosonic ``spinons'' and Ising vortices or ``visons''. We use an Ising duality transformation to express vison correlators as non-local strings in terms of the spin operators, and calculate the string correlators using the ground state wavefunction of the modified Hamiltonian. Remarkably, this wavefunction is exactly given by a kind of Gutzwiller projection of an XY ferromagnet. Finally, we show that the deconfined spin liquid state persists over a finite range as the additional four-spin interaction is reduced, and study the effect of this reduction on the dynamics of spinons and visons.

First-order phase transition in ferroelectric superlattice described by the transverse Ising model

The phase transition properties of a ferroelectric/ferroelectric superlattice described by the transverse Ising model, by taking into account the four-spin interactions have been studied with parameters imitating PbTiO 3/BaTiO 3. The period dependence of the Curie temperature of the superlattice is given. The phase transition behavior of the polarization and the susceptibility are calculated, which show the feature of first-order phase transitions. A ferroelectric–ferroelectric phase transition at low temperature is found for large-period superlattice.

THREE-DIMENSIONAL GONIHEDRIC SPIN SYSTEM

We perform Monte–Carlo simulations of a three-dimensional spin system with a Hamiltonian which contains only four-spin interaction term. This system describes random surfaces with extrinsic curvature – gonihedric action. We study the anisotropic model when the coupling constants βS for the space-like plaquettes and βT for the transverse-like plaquettes are different. In the two limits βS = 0 and βT = 0 the system has been solved exactly and the main interest is to see what happens when we move away from these points towards the isotropic point, where we recover the original model. We find that the phase transition is of first order for βT = βS ≈ 0.25, while away from this point it becomes weaker and eventually turns to a crossover. The conclusion which can be drawn from this result is that the exact solution at the point βS = 0 in terms of 2D-Ising model should be considered as a good zero-order approximation in the description of the system also at the isotropic point βS = βT and clearly confirms the earlier findings that at the isotropic point the original model shows a first-order phase transition.

Exact results of a doubly decorated ising model with four-spin interactions

A doubly decorated Ising model with the crystal-field, two—and four-spin interactions is studied by applying the standard decoration-iteration transformation. Exact results for the critical boundaries, compensation temperatures and magnetization of the system are discussed in detail.

Magnetic order in the frustrated Heisenberg model for the fcc type-I configuration

The Heisenberg model for the fcc type-I configuration with various types of interactions is studied with use of the noninteracting spin-wave theory. It is shown that local anisotropy, four-spin exchange interactions, and biquadratic interactions can lift the continuous degeneracy of the ground state through the stabilization of a noncollinear magnetic state. Moreover, in the particular case of a pyrite structure, a Dzyaloshinsky-Moriya term or a symmetric anisotropic exchange stabilizes the double-$\mathbf{k}$ configuration. The single-$\mathbf{k}$ state is also discussed. We prove, in particular, that quantum fluctuations favor such a case. Consequences for the magnetic moment reduction and for the spin-wave spectra of the presence of such stabilizing terms are calculated and compared with data. Experiments seem to indicate that the minimal model built from the nearest-neighbor Heisenberg interaction and a stabilizing term is not satisfactory.

Observation of a spin wave exponent of 5/2 in the uniaxial antiferromagnet MnF 2

The temperature dependence of the sublattice magnetization (order parameter) of the uniaxial antiferromagnet MnF 2 ( S=5/2) has been measured using 19F NMR, neutron scattering and magnetic X-ray scattering. All three methods reveal a T 5/2 power law for the deviation of the order parameter from its saturation value at absolute zero. This law holds perfectly up to 0.8 of the Néel temperature, T N=67.2 K. The unexpected spin wave exponent of 5/2 as well as the large validity range of the T 5/2 power law indicate that the spin dynamics deviates from that of classical spin wave theories. We propose that fourth-order exchange interactions, i.e., biquadratic, three- and four-spin interactions are responsible for this. Existence of these interactions is evidenced with measurements of the cubic susceptibility χ 3. Surprisingly, χ 3 is negative for all temperatures (the magnetic isotherms increase faster than linearly with field) meaning that the fourth-order interactions are ferromagnetic. Since χ 3 is large but does not diverge at T N the existence of a long range ferromagnetically ordered component is questionable. The new quantum exponent of 5/2 is considered as characteristic for magnets with half-integral spin and axial interactions. This result completes the empirical systematics of the spin wave exponents in materials with half-integral spin. These exponents are 2 for isotropic interactions, 3/2 for anisotropic and/or two-dimensional interactions and 5/2 for axial interactions.

Properties of ferroelectric thin films with a first-order phase transitions

A Green's function technique is used to investigate the properties of ferroelectric thin films with a first-order phase transitions on the basis of the transverse Ising model. Taking into account the four-spin interactions beside the two-spin interactions the dependence of the polarization on film thickness and temperature and the thickness dependence of the Curie temperature become more complicated.