Three-spin Model Research Articles

Spin glasses without time-reversal symmetry and the absence of a genuine structural glass transition

We study the three-spin model and the Ising spin glass in a field using the Migdal-Kadanoff approximation. The flows of the couplings and fields indicate no phase transition, but they show even for the three-spin model a slow crossover to the asymptotic high-temperature behavior for large values of the coupling. We have also evaluated a quantity that is a measure of the degree of non-self-averaging, and we found that it can become large for certain ranges of the parameters and the system sizes. For a spin glass in a field the maximum of non-self-averaging follows a line for given system size that resembles the de Almeida-Thouless line. We conclude that non-self-averaging found in Monte Carlo simulations cannot be taken as evidence for the existence of a low-temperature phase with replica symmetry breaking. Models similar to the three-spin model have been extensively discussed in order to provide a description of structural glasses. Their theory at mean-field level resembles the mode-coupling theory of real glasses. At that level the approach via one-step replica symmetry breaking predicts two transitions, the first transition being dynamic and the second thermodynamic. Our results suggest that in real finite-dimensional glasses there will be no genuine transitions at all, but that some features of mean-field theory could still provide some useful insights.

Cross-relaxation dynamics between laser-polarized xenon and a surface species using a simple three-spin model

We present an analysis of the cross-relaxation dynamics between optically polarized 129 Xe and surface 13 C and 1 H spins in methanol adsorbed on a SiO 2 surface. Analytical expressions for the 13 C polarization are derived, which show that the 13 C polarization is determined by cross-relaxation with both 129 Xe and 1 H spins. The 1 H spins act as a polarization sink; however, saturation of the protons results in a further increase in signal intensity. Replacing the 1 H spin reservoir with 2 H increases the 13 C signal by a factor of 12 (25 as compared to room-temperature data). Further improvements are anticipated using higher-powered lasers.

Syntheses and Magnetic Properties of Stable Organic Triradicals with Quartet Ground States Consisting of Different Nitroxide Radicals

Bis[p-(1-oxyl-3-oxide-4,4,5,5-tetramethylimidazolin-2-yl)phenyl] nitroxide (3) was synthesized via desilylation of O-protected diradical followed by autoxidation. By deoxgenation of 3, p-(1-oxyl-4,4,5,5-tetramethylimidazolin-2-yl)phenyl-p-(1-oxyl-3-oxide-4,4,5,5-tetramethylimidazolin-2-yl)phenyl nitroxide (4) and bis[p-(1-oxyl-4,4,5,5-tetramethylimidazolin-2-yl)phenyl] nitroxide (5) were prepared. X-ray analysis of a dark brown needle single crystal for 4 confirmed that 4 consisted of three different kinds of nitroxide radical centers, which showed three reversible redox waves at +0.42, +0.82, and +1.01 V (vs Ag/Ag+) in CH3CN solution. The temperature dependence of the molar magnetic susceptibilities for microcrystalline samples of triradicals 3−5 was measured by a SQUID susceptometer, showing the intramolecular ferromagnetic and intermolecular antiferromagnetic interactions. Experimental data were fitted to the equation derived from an asymmetric linear three-spin model (H = −2(J12S1·S2 + J23S2·S3)). The best fit parameters were J12/kB = J23/kB = 231 ± 4 K for 3, J12/kB = 349 ± 26 K, J23/kB = 130 ± 3 K for 4, and J12/kB = J23/kB = 127 ± 3 K for 5. Triradicals 3−5 thus have quartet ground states. These exchange coupling parameters are mutually compared in reference to their molecular structures.

Homonuclear Separated Local-Field Spectroscopy by Magnetization-Exchange NMR

The possibility to perform homonuclear separated-local field NMR spectroscopy by magnetization-exchange is presented. Solid-state one-dimensional proton magnetization-exchange NMR is used to investigate intergroup residual dipolar couplings in cis-1,4-polybutadiene elastomer. A three-spin model is employed, in which the CHand CΗ2-protons are considered to be coupled by residual dipolar interactions. The magnetization-exchange process between the CHand the CΗ2-group in the regime of short mixing time provides valuable insight regarding molecular order. The spin-system response reflects well-localized dipolar interactions. The residual intergroup dipolar couplings are measured along the average polymer-chain direction for different temperatures. The dynamic order parameter along the chains is also evaluated. PACS numbers: 33.25.+k, 61.41.+e

Two-dimensional proton magnetization-exchange NMR spectroscopy in cross-linked elastomers

Solid-state two-dimensional proton magnetization-exchange NMR is used to investigate intergroup residual dipolar couplings in a cross-linking series of poly(styrene-cobutadiene) elastomers. The magnetization-exchange process between the CH and the CH2 group in the regime of short mixing time provides valuable insight regarding molecular order. A three-spin model is employed, in which the CH and CH2 protons are considered to be coupled by residual dipolar interactions. The spin-system response reflects well-localized dipolar interactions. The time scale in which the exchange process takes place justifies these assumptions as well as the interpretation of various NMR relaxation experiments previously performed on this class of polymers. The residual intergroup dipolar couplings are measured along the average polymer-chain direction and correlated with the dynamic storage modulus. It is shown that they are sensitive to both cross-link points and nonpermanent geometric constraints of the chain motion. The dynamic order parameter along the chains is evaluated. It exhibits the remarkably high value of 〈P2〉≊0.13 for the carbon–carbon bond connecting the CH and the CH2 groups in polybutadiene in the uncross-linked copolymer melt and only slightly increases with the cross-link density.

Spin catalysis: three-spin model

Recently it has been shown that in a radical triad one of the radical partners affects the chemical reactivity of the other pair, catalyzing the spin transformation of this pair. The phenomenon is shown to be caused by the exchange interaction between the radical triad partners which stimulates doublet-doublet spin evolution and produces the oscillating triplet-singlet spin conversion of the selected radical pair in the radical triad under the influence of the odd radical spin. The theory of the phenomenon is developed and the equations for the rate of spin evolution in a three-spin system are derived. A new type of quantum beats is predicted.

Electron spin polarization in the donor triplet state of bacterial photosynthetic reaction centres. II. Anisotropic inversion of electron spin polarization in a three-spin model reaction centre

An explanation is proposed for the electron spin polarization pattern in the Δm S = ± 1 EPR spectrum of the donor triplet state in pre-reduced Rhodopseudomonas viridis reaction centres at temperatures above 20 K. Calculations based on a simple model of the reaction centre indicate that rapid spin-lattice relaxation of the iron-semiquinone complex (Q A −Fe 2+) can perturb the polarization of the donor triplet provided the EPR frequency of Q A −Fe 2+ is close to that of P + (the cation of the primary donor) and I − (the anion of the intermediary acceptor). In agreement with experimental observations, this mechanism only operates in the presence of a large exchange interaction between I − and Q A −Fe 2+. The observed anisotropy of this effect is attributed to the anisotropy of the resonance frequency of Q A −Fe 2+.

The Ising magnet with three-site four-spin interaction

For the Ising ferromagnet with S=3/2 and S=1, the effects of the three-site four-spin interaction J'(Si.Sj)(Sj.Sk) on the magnetisation (Sz) and the Curie temperature TC have been calculated by the use of the three-spin model approximation. The temperature dependences of (Sz) and (Sz3) turn out to show an abnormal behaviour for the three-site four-spin interaction in the range J'<or approximately=-J/(2(z-1)S2), where J is the usual bi-linear exchange parameter and z is the coordination number. It is also pointed out that this abnormal behaviour of (Sz) is very pronounced in the low-temperature region. This abnormal low-temperature behaviour may signal a crossover to a complex antiferromagnetic ground state such as found in the systems with negative multi-spin interactions. Furthermore, the three-site four-spin interaction J' is shown to affect the Curie temperature TC mainly, and for the Ising ferromagnet with S=3/2 on the body-centred cubic lattice the change Delta TC/TC0 in the Curie temperature is shown to be about 50% at J'=-0.025J. It is also clear that three-site four-spin interaction has a larger effect on the magnetism of the Ising ferromagnet with a large spin and large coordination number.

Spin-one Ising ferromagnet with three-site four-spin interaction

For the Ising ferromagnet with S = 1 the effects of the three-site four-spin interaction J′ on the magnetization and the Curie temperature have been calculated using the three-spin model approximation and its effect is shown to be significant for negative value of J′.

Series expansion study of first- and second-order phase transitions in a model with multispin coupling

The type of phase transition in a chain of Ising spins with multispin interaction is studied in a transverse field, using strong- and weak-coupling expansions. The transition is shown to be of first order if more than three spins are coupled. The critical exponents for the three-spin coupling model are estimated.

Numerical evidence for two critical points in a triplet Ising model

It is shown that numerical data recently used to evaluate the residual entropy of Kagome ice can be adapted to form an expansion for the zero field free energy of a three-spin Ising model on a triangulated dice lattice. The expansion is used to test a recent conjecture of Wu (see J. Phys. C: Solid St. Phys. vol.7, p.181) that this model should exhibit two phase transitions.

The three-spin Ising model as an eight-vertex model

The three-spin Ising model is related to a special case of the eight-vertex model by a spin transformation. It follows that the models have the same free energy magnetization and polarization.

Duality relation for 32-vertex model on the triangular lattice

The duality relation is derived for a vertex model on the triangular lattice. Vertex configurations are limited to the 32 that have an odd number of incoming arrows, and vertex energies are invariant to rotations ofp/3 and reversal of all arrows. Special cases of the model include the triangular Ising model and Baxter's three-spin model, for each of which the duality relation gives the critical temperature.

32-vertex model on the triangular lattice

The 32-vertex model on a triangular lattice is solved exactly in two special cases. In one case the model is reducible to a three-spin Ising model and has the exponents alpha = alpha '=2/3. The other soluble case is the free-fermion model which exhibits the Ising behaviour but may possess multiple transitions.