Four-spin Coupling Research Articles

Study of the Critical Behavior and the Multi-Layer Transition in a Spin-1 Ashkin–Teller Model under the Effect of the RKKY Interaction: Finite-Size-Scaling and Monte Carlo Studies

By using a Monte Carlo simulation, we have studied the effects on the multilayer transition and magnetic properties of the crystal field [Formula: see text], the four-spin coupling [Formula: see text] and RKKY interaction in the spin-1 Ashkin–Teller (AT) model of a system composed of two magnetic multi-layer materials, of various thicknesses, separated by a nonmagnetic spacer of thickness [Formula: see text]. By varying the strength of [Formula: see text], we have obtained a new partially ordered phase [Formula: see text], for different values of [Formula: see text]. We have established a rich phase diagram with first and second-order phase transitions with tricritical points. It is shown that the transition temperature of both magnetic blocks depends strongly on the thickness of the magnetic layers [Formula: see text], as well as [Formula: see text] and [Formula: see text]. There exists a critical thickness of the magnetic layers [Formula: see text] above which the multilayer blocks undergo a transition separately at different temperatures, for a high value of [Formula: see text] and [Formula: see text]. Besides, the critical exponents are computed.

Critical behavior of the Ashkin–Teller model with a line defect: Towards reconciliation between numerical and analytical results

We study magnetic critical behavior in the two-dimensional Ashkin–Teller model with an asymmetric defect line. This system is represented by two Ising lattices of spins σ and τ interacting through a four-spin coupling ε. In addition, the couplings between σ-spins are modified along a particular line, whereas couplings between τ-spins are kept unaltered. This problem has been previously considered by means of analytical field-theoretical methods and by numerical techniques, with contradictory results. For ε>0 field-theoretical calculations give a magnetic critical exponent corresponding to σ-spins which depends on the defect strength only (it is independent of ε), while τ-spins magnetization decay with the universal Ising value 1/8. On the contrary, numerical computations based on density matrix renormalization (DMRG) give, for ε>0 similar scaling behaviors for σ and τ spins, which depend on both ε and defect intensity. In this paper we revisit the problem by performing a direct Monte Carlo simulation. Our results are in good agreement with DMRG computations. By reexamining the field-theoretical approach, we show how numerical and analytical results can be reconciled when a more general regularization prescription is adopted.

Magnetic properties and phase diagrams of the spin-1 Ashkin Teller model ferromagnetic thin films in the presence of a crystal field

Using Monte Carlo simulations based on the Metropolis algorithm, we have investigated magnetic properties and phase diagrams of the spin-1 Ashkin Teller model ferromagnetic thin films. The effects of the crystal field D/J2b and four-spin coupling (J4s/J2b, J4b/J2b) has been studied in detail. Therefore, the phase diagrams in the (kBTc/J2b,J2s/J2b) plane exhibits the special point (Rs=J2s/J2b)sp, for different values of D/J2b and (J4s/J2b, J4b/J2b), wherein all film thicknesses having the same critical temperature. In addition, the magnetization profiles present a first order phase transition behavior. Then, we found rich phase diagrams with first- and second-order phase transitions that meet at tricritical points that are dependent on the film thickness N. Finally, this model presents a new partially ordered phase 〈σS〉, between the paramagnetic phase and the Baxter phase, which are separated by a second-order phase transition, for positive values of D/J2b and for each film thickness N.

Multi-layer transition and the magnetic properties of a spin-1/2 Ashkin Teller model with RKKY interaction: A Monte Carlo study

The effects of RKKY interaction and the influence of the four spin interaction J4, on the multi-layer transition and magnetic properties of a spin-1/2 Ashkin Teller model of a ferromagnetic system shaped by two magnetic multi-layer materials, of different thicknesses, separated by a non-magnetic spacer of thickness M, are examined using Monte Carlo simulations. The system presents a new partially ordered phase <σS>, for various values of J4/J2, and exhibits behavior typical of a second-order phase transition. It is found that the transition temperatures of the two blocks are strongly dependent on the thickness of the magnetic layers N and the four-spin coupling J4/J2, while they do not depend on the non-magnetic spacer and the Fermi level kf. Finally, We have obtained a critical thickness ML of the non-magnetic spacer above which the multi-layer blocks undergo a transition separately at different temperatures, for J4/J2=3 and kf=0.2.

Optically induced cross relaxation via nitrogen-related defects for bulk diamond C13 hyperpolarization

In this Rapid Communication we utilize nuclear magnetic resonance to investigate the hyperpolarization effect of negatively charged nitrogen vacancy (NV) centers on bulk $^{13}\mathrm{C}$ nuclei in a diamond single crystal. We were able to identify several polarization peaks of a different sign at different magnetic fields in a region of some tens of Gauss centered around $50\phantom{\rule{0.28em}{0ex}}\mathrm{mT}$. The bulk $^{13}\mathrm{C}$ hyperpolarization in the investigated field range is usually attributed to the excited state level anticrossing of the NV center. However, we found that this bulk hyperpolarization is caused by optically induced cross relaxation and that it takes place in the NV center ground state. The four-spin coupling between the polarized NV electron spin, the electron spin of a substitutional nitrogen impurity (P1), as well as its $^{14}\mathrm{N}$ nuclei and the $^{13}\mathrm{C}$ nuclear spin have to be considered. We introduce a simple theoretical model which completely fits with the experimental data and which clearly shows that the P1 centers are involved in the polarization process. We expect that the current work has a significant impact on future NV-based polarization applications.

Continuum of compensation points in the mixed spin Ising ferrimagnet with four-spin interaction and next-nearest neighbor coupling

ABSTRACTWe investigate the magnetic properties of the mixed spin-1/2 and spin-1 Ising ferrimagnetic system with four-spin interaction J4 and next-nearest neighbor (NNN) coupling J′. We perform exact ground-state calculations and use the finite cluster approximation, based on a single cluster theory, to derive the state equations for the two-dimensional square lattice. The main attention has been paid to the study of the phase diagram for both the transition and compensation temperatures. We find a number of characteristic behaviors. The model with only NNNs induces one compensation point while the four-spin interaction does not. The investigation of the model with both interactions shows a number of characteristic behaviors. In particular, the presence of the four-spin interaction, according to J4 and J′, may lead to one, two or possibly a continuum of compensation points. This phenomenon may have important applications in technology such as thermomagnetic writing and erasing at the compensation point.

The effect of quenched bond disorder on first-order phase transitions

We investigate the effect of quenched bond disorder on the two-dimensional three-color Ashkin–Teller model, which undergoes a first-order phase transition in the absence of impurities. This is one of the simplest and striking models in which quantitative numerical simulations can be carried out to investigate emergent criticality due to disorder rounding of first-order transition. Utilizing extensive cluster Monte Carlo simulations on large lattice sizes of up to 128×128 spins, each of which is represented by three colors taking values ±1, we show that the rounding of the first-order phase transition is an emergent criticality. We further calculate the correlation length critical exponent, ν, and the magnetization critical exponent, β, from finite size scaling analysis. We find that the critical exponents, ν and β, change as the strength of disorder or the four-spin coupling varies, and we show that the critical exponents appear not to be in the Ising universality class. We know of no analytical approaches that can explain our non-perturbative results. However our results should inspire further work on this important problem, either numerical or analytical.

Bond Disorder Induced Criticality of the Three-Color Ashkin-Teller Model

An intriguing result of statistical mechanics is that a first-order phase transition can be rounded by disorder coupled to energylike variables. In fact, even more intriguing is that the rounding may manifest itself as a critical point, quantum or classical. In general, it is not known, however, what universality classes, if any, such criticalities belong to. In order to shed light on this question we examine in detail the disordered three-color Ashkin-Teller model by Monte Carlo methods. Extensive analyses indicate that the critical exponents define a new universality class. We show that the rounding of the first-order transition of the pure model due to the impurities is manifested as criticality. However, the magnetization critical exponent, β, and the correlation length critical exponent, ν, are found to vary with disorder and the four-spin coupling strength, and we conclusively rule out that the model belongs to the universality class of the two-dimensional Ising model.

Quantum criticality in SU(3) and SU(4) antiferromagnets

We study the quantum phase transition out of the N\'eel state in SU(3) and SU(4) generalizations of the Heisenberg antiferromagnet with a sign-problem-free four-spin coupling (so-called $JQ$ model), by extensive quantum Monte Carlo simulations. We present evidence that the SU(3) and SU(4) order parameters and the SU(3) and SU(4) stiffness go to zero continuously without any evidence of a first-order transition. However, we find considerable deviations from simple scaling laws for the stiffness even in the largest system sizes studied. We interpret these as arising from multiplicative scaling terms in these quantities that affect the leading behavior, i.e., they will persist in the thermodynamic limit, unlike the conventional additive corrections from irrelevant operators. We conjecture that these multiplicative terms arise from dangerously irrelevant operators whose contributions to the quantities of interest are nonanalytic.

Monte Carlo Simulation of First Order Phase Transitions

Monte Carlo simulation with Metropolis algorithm has been performed on a cubic Ising lattice with four-spin couplings. Temperature dependence of the spin average and average energy has been obtained. We found that the phase transition is of first order when the strength of four-spin coupling is stronger a critical value, and this critical value is of lattice size dependence. Binder cumulants still can be used to determine the second order phase transition temperature. For first order phase transition, the spin average disappears abruptly at the temperature of the average energy being a third of the ground state energy.

Ground-state phases and quantum phase transitions in a two-dimensional spin-1/2 XY model with four-spin interactions

We discuss the ground state phase transition between an antiferromagnet and a valence-bond solid in a two-dimensional spin-1/2 XY model with a four-spin interaction. This transition has been proposed as a candidate for a deconfined quantum-critical point. We analyze quantum Monte Carlo data in order to accurately characterize the transition. The central question that remains to be answered is whether the transition really is continuous, or whether it is actually weakly first-order. We present the current status of both ground state and finite-temperature calculations. Based on the results, we discuss possible scenarios for the transition, none of which is consistent with deconfined quantum-criticality. However, we argue that a deconfined quantum-critical point may be located nearby in an extended parameter space.We also discuss the staggered Ising phase obtaining in the limit of strong four-spin coupling.

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.

Magnetic ordering in doped coupled frustrated quantum spin- [formula omitted] chains with four-spin exchange

The role of various magnetic inter-chain couplings has been investigated recently by numerical methods in doped frustrated quantum spin chains. A non-magnetic dopant introduced in a gapped spin chain releases a free spin- 1 2 soliton. The formation of a local magnetic moment has been analyzed in term of soliton confinement. A four-spin coupling which might originate from cyclic exchange is shown to produce such a confinement. Dopants on different chains experience an effective space-extended non-frustrating pairwise spin interaction. This effective interaction between impurity spins is long ranged and therefore is expected to play a crucial role in the mechanism of antiferromagnetic long-range ordering observed in spin-Peierls compounds such as CuGeO 3 doped with non-magnetic impurities.

Doped coupled frustrated spin-1/2 chains with four-spin exchange.

The role of various magnetic interchain couplings is investigated by numerical methods in doped frustrated quantum spin chains. A nonmagnetic dopant introduced in a gapped spin chain releases a free spin-1/2 soliton. The formation of a local magnetic moment is analyzed in terms of soliton confinement. A four-spin coupling which might originate from cyclic exchange is shown to produce such a confinement. Dopants on different chains experience an effective space-extended nonfrustrating pairwise spin interaction.

Lebowitz inequalities for Ashkin–Teller systems

We consider the Ashkin–Teller model with negative four-spin coupling but still in the region where the ground state is ferromagnetic. We establish the standard Lebowitz inequality as well as the extension that is necessary to prove a divergent susceptibility.

Parallel dynamics of the asymmetric extremely diluted Ashkin-Teller neural network

The parallel dynamics of the asymmetric extremely diluted Ashkin-Teller neural network is studied using signal-to-noise analysis techniques. Evolution equations for the order parameters are derived, both at zero and finite temperature. The retrieval properties of the network are discussed in terms of the four-spin coupling strength and the temperature. It is shown that the presence of a four-spin coupling enhances the retrieval quality.

Large-Nlimit of theXY-Ashkin-Teller model: solution in two dimensions

We introduce a vector model coupled to an N-colour Ashkin-Teller model and solve its phase diagram in the large-N limit in two dimensions. It is shown that the transition line starts from the axis of Ising couplings with a behaviour which can be critical or first order depending on the strength of the four-spin coupling and of the coupling between spin and vector variables. Below a negative value of the four-spin coupling the transition is always continuous.

The derivation of the free energy of the ising model from that of the eight-vertex model

The zero-field eight-vertex model is equivalent to a square lattice Ising model, with a four-spin coupling and second neighbour coupling but no nearest neighbour coupling. When the four-spin coupling is zero, the model reduces to two decoupled nearest neighbour Ising models. The standard formula for the free energy of the Ising model is, therefore, implicit in Baxter's expression for the free energy of the zero-field eight-vertex model. The detailed derivation of this result has not appeared in print. As a footnote to Baxter's work this paper provides the necessary analysis.

SPONTANEOUS MAGNETIZATION OF THE ISING MODEL ON THE ASANOHA LATTICE

We have derived exactly the spontaneous magnetization of the Ising model on the Asanoha (hemp leaf) lattice with nine two-spin coupling constants, two four-spin coupling constants, and three magnetic moments. The dual lattice of the 3–12 lattice is the Asanoha lattice which includes the triangular lattice and the diced lattice as special cases.

Ising model with two-, three- and four-spin interactions

The two-state Ising model with nearest-neighbour bilinear exchange constant J(2), three-spin coupling constant J(3) and four-spin coupling constant J(4) is studied using the effective-field approximation. The temperature variation in spontaneous magnetization is studied for different coordination numbers z and for various values of the parameters alpha =J(3)/J(2) and alpha '=J(4)/J(2). It is seen that, in the absence of three-spin coupling, there exists a critical value of alpha ' (say, alpha 'c) above which the magnetization becomes double valued at and beyond the Curie temperature Tc, forming a bulge near Tc which indicates the occurrence of a first-order transition. The expressions for alpha 'c for z=3, 4, 6 are derived and it is found that alpha 'c increases as z increases. In the absence of four-spin coupling it is found that first-order transitions appear for alpha >or=0. The magnetization curves are also studied for the case when all the interactions are present. The results are discussed with reference to those obtained from the molecular-field approximation.