Non-local specific heat — Ordered-phase results

The energy-energy correlation function C(k) is calculated for general n-component spin systems in a resummed one-loop approximation. The Goldstone mode singularities are resummed in a manner consistent with exactly known limits.     

Critical behavior of anisotropic cubic systems with long- and short-range interactions

Critical phenomena in anisotropic cubic N-component spin systems with long- and short-range interactions are investigated and discussed in the regions of weakly long-range, intermediate-range, range, and the long-range potentials. The expressions for the eigenvalues and the critical exponents (n,γ and crossover exponents) in these three regions are derived and their stability is discussed. These results of the systems are compared with those of the same isotropic systems.     

Adsorption of gas mixtures on heterogeneous surfaces: The integral representation for a monolayer total adsorption isotherm

The authors extended the integral equation for a one-component adsorption isotherm on to n-component adsorption from gaseous mixtures. It appears that the n-component adsorption isotherm on heterogeneous surfaces can be presented as a multiple integral. Two methods were used for evaluation of the surface heterogeneity with regard to a gas mixture. The first method is based on the n-dimensional gaussian energy distribution. The second one concerns the extension of our method for studying adsorption systems of high surface heterogeneity. Two-component adsorption systems have been analyzed in details.     

Statistical mechanics of systems of unbounded spins

We develop the statistical mechanics of unboundedn-component spin systems on the latticeZ ^v interacting via potentials which are superstable and strongly tempered. We prove the existence and uniqueness of the infinite volume free energy density for a wide class of boundary conditions. The uniqueness of the equilibrium state (whose existence is established in general) is then proven for one component ferromagnetic spins whose free energy is differentiable with respect to the magnetic field.     

Crossover behavior of anisotropic cubic system with ionic anisotropy

Crossover behavior of anisotropic cubic N-component spin system with ionic anisotropies of different magnitude is studied in terms of the renormalization-group (RG) approach in momentum space. As a fundamental case, we choose a system with two kinds of strength of ionic anisotropies (i.e. m²₁ for the M-component spin and m²₂ for the other (N–M)-one), which has a bicritical point. We discuss the critical behavior and crossover behavior between the M- component system and the N-component system on the critical exponents [i.e., coefficient functions appearing in the RG equation of γS for the spin field S, γS² for the S²-field and γδS² for the δS² (≡[(N-M)S²₂-MS²₂]/N)-field] and on the temperature-dependent crossover exponent γeff.     

Crossover exponent to order ϵ3(ϵ = 4 − d) in isotropic N-component spin systems

The crossover exponent ø to the order ?³ in isotropic N-component spin systems is derived by means of the Callan-Symanzik equations. The result obtained coincides with that by Hikami and Abe in the spherical limit, is in good agreement with that by means of series expansions by Pfeuty et al. in three dimensions and shows an oscillating behavior about some values with the degrees of expansion in ?.     

Final state interaction as the main mechanism of double hole creation in atomic K shells during electromagnetic nuclear decays

Large violations of the OZI-rule have been observed in pp-annihilation into ? mesons when the initial state is in triplet spin configuration. One possible explanation for this phenomenon is that this is due to a small negatively polarized ss?-component in the nucleon which has been found in polarized deep inelastic scattering of leptons. In the nonperturbative region there is little experimental information on the sign of Δs. We show by spin projection conservation arguments that if the ?-production enhancement in the p?p → ?π is due to the transfer of a ss? from the initial nucleon to the final ?, then Δs must be preferentially positive. We study polarization phenomena in the process N + N → + N+ V⁰ where V⁰ is a vector meson near threshold and we show that a comparison of the pp → pp? reaction (which is dominated by a spin triplet in the initial state, at threshold) and the np → np? (which is driven by non-interfering spin triplet and spin singlet amplitudes) would test quantitatively the ss?-driven spin triplet dominance. Finally we discuss the possibility of using the relationship between the Gerasimov-Drell-Hearn sum-rule and the integral of the spin structure function g_1p to measure the polarization of the ss?-component at low momentum transfer.     

Upper bounds on the transition temperature of classical n.n. ferromagnetic systems for general n and d

A differential equation is obtained for the spin-spin correlation function of a system of n-component classical spins interacting via a nearest neighbour ferromagnetic interaction. The differential equation makes it possible to obtain upper bounds on the correlation length and the transition temperature. It also makes it possible to relate the correlation length with the energy per spin and to obtain a necessary condition for the existence of the phase transition in terms of the energy per spin.     

Analysis of the sequence of insulator-metal phase transitions at high pressure in systems with spin crossovers

Possible variants of the Mott-Hubbard phase transitions at high pressure in systems with spin crossovers are considered. Owing to the universal character of the dependence of the effective Hubbard parameter U _eff(d ⁿ ) on the average number of d electrons, which is determined by the presence of spin crossovers, cascades of insulator-metal-insulator phase transitions in systems with d ³, d ⁶, and d ⁸ configurations become possible. Moreover, the systems with d ⁶ configuration can exhibit transitions from a metal in the absence of external pressure to an insulator at high pressure.     

Critical exponent η of isotropic spin systems with long and short-range interactions

Critical phenomena, in particular, the critical exponent η, in isotropic N-component spin systems with long and short range interactions are discussed in the regions of the weakly long-range, the intermediate-range, and the long-range potentials. The expressions for η in these three regions are derived and their stability is discussed.     

Long-range potentials and the electromagnetic polarizabilities

The long-range spin and velocity independent forces of electromagnetic origin which act between any two systems are studied for those cases in which no forces of this type exist to order e². It is shown that they are uniquely determined by the charge, magnetic moment, and polarizabilities of both systems, not only to the dominant order r^?n, but also to the next one r^?(n+1). These potentials provide the link between Compton scattering polarizabilities (response to real photons) and classically defined polarizabilities (response to static electromagnetic field). The two definitions are shown to be equivalent for neutral spinless systems; the problems arising for a neutral particle with magnetic moment are studied in detail. The r^?(n+1) terms have no classical counterpart, since they are due to the relativistic quantum propagation of the system which carries charge or magnetic moment. The results are of general validity with analyticity, crossing, unitarity, and gauge invariance as only inputs. The most general conclusion is that the polarizabilities represent electromagnetic properties of a system at order e², as the charge and magnetic moment do at order e. Thus they give the strength of the response to electric and magnetic fields, independently of the specific characteristics of the electromagnetic agent.     

Absorption and dispersion of electromagnetic eigenwaves of electron-positron plasma in a strong magnetic field: H. Pérez Rojas and A. E. Shabad. Instituto de Investigación Técnica Fundamental,Havana, Cuba

Quantum theories of N-component Fermi fields are formulated in terms of overcomplete sets of bilocal pseudo-spin operators in analogy with the Holstein-Primakoff theory of ordinary spin systems. Classical constrained Hamiltonian systems arise in the large N limit revealing the semi-classical nature of the large N approximation. Such systems are briefly analyzed in the context of the Gross-Neveu $\text{(}\text{ψ}\text{ψ)}{}^2$ model, where the dynamics of c-number (rather than Grassman) fields governs the semi-classical limit.     

On the Mass Difference between π and ρ Using a Relativistic Two-Body Model

The big mass difference between the pion (π) and rho meson (ρ) possibly originates from the spin-dependent nature of the interactions in the two states since these two states are similar except for spin. Both π and ρ are quark-antiquark systems which can be treated using the two-body Dirac equations (TBDE) of constraint dynamics. This relativistic approach for two-body system has the advantage over the non-relativistic treatment in the sense that the spin-dependent nature is automatically coming out from the formalism. We employed Dirac’s relativistic constraint dynamics to describe quark-antiquark systems. Within this formalism, the 16-component Dirac equation is reduced to the 4-component 2nd-order differential equation and the radial part of this equation is simply a Schrödinger-type equation with various terms calculated from the basic radial potential. We used a modified Richardson potential for quark-antiquark systems which satisfies the conditions of confinement and asymptotic freedom. We obtained the wave functions for these two mesons which are not singular at short distances. We also found that the cancellation between the Darwin and spin-spin interaction terms occurs in the π mass but not in the ρ mass and this is the main source of the big difference in the two meson masses.     

Second moment of multiple-quantum NMR and a time-dependent growth of the number of multispin correlations in solids

The time evolution of multispin correlations (the growth of the number of correlated spins as a function of time) can be observed directly using the multiple-quantum nuclear magnetic resonance spectroscopy of solids. A quantity related to this number, namely, the second moment 〈n ²(t)〉 of the intensity distribution of coherences of different orders in the multiple-quantum spectrum can be calculated using the theory proposed in this work. An approach to the calculation of the four-spin time correlation function through which this moment is expressed is developed. The main sequences of contributions in the expansion of this function into a time power series are summed using the approximation of a large number of neighbors both for systems with a secular dipole-dipole interaction and for systems with a nonsecular effective interaction. An exponential dependence of 〈n ²(t)〉 is obtained. The value of 〈n ²(t)〉 is additionally calculated using an expansion in terms of orthogonal operators for three model examples corresponding to different limiting realizations of spin systems. It is shown that the results of the microscopic theory at least qualitatively agree with both the results obtained for model examples and experimental results obtained recently for adamantane.     

Elastic scattering of20Ne on24Mg

High spin states in⁸⁵Rb and⁸⁵Sr were populated in the reactions⁷⁶Ge(¹²C,p2n) and⁷⁶Ge(¹²C,3n), respectively. The lifetimes of twelve states were measured via the recoil distance Doppler shift technique. The positive parity bands in both nuclei associated with theg _9/2 orbit exhibit decrasingE2 strengths for increasing spin value marking the onset of multiparticle excitation.     

Correlation inequalities and contour estimates

We give a simple estimate on the probability of contours in classical ferromagnetic spin systems, based on Griffiths' or Ginibre's correlation inequalities. This includes quite general one- and two-component spin models. Some extension also holds for alln-component anisotropic or isotropic rotators.Supported by NSF grant No. MCS78-01885.On leave from: Institut de Physique Théorique, Université de Louvain, Belgium.Supported by NSF grant No. PHY78-15920.     

Quantum registers based on single NV + <Emphasis Type="Italic">n</Emphasis><Superscript>13</Superscript>C centers in diamond: II. Spin characteristics of registers and spectra of optically detected magnetic resonance

The spin Hamiltonian method in combination with ab initio calculations of the spin characteristics of quantum registers that include an electron spin S = 1 of a single NV center in the ground electronic state and nuclear spins I = 1/2 of several atoms ¹³C located at different lattice sites near the vacancy of the NV center is applied to find eigenvalues and eigenfunctions of spin systems NV + n ¹³C for cases where the lattice sites nearest to the vacancy of the NV center contain one, two, or three ¹³C nuclear spins, as well as for cases where ¹³C atoms are located at sites more distant from the vacancy. For these single spin NV + n ¹³C systems, the spectra of optically detected magnetic resonance (ODMR) are calculated, which agree well with available experimental data.     

Theoretical evaluation of the electron paramagnetic resonance spin Hamiltonian parameters for the impurity displacements for Fe3+ and Ru3+ in corundum

The impurity displacements for Fe³⁺ and Ru³⁺ in corundum (Al₂O₃) are theoretically studied using the perturbation formulas of the spin Hamiltonian parameters (zero-field splitting and anisotropic g factors) for a 3d⁵ (with high spin S = 5/2) and a 4d⁵ (with low spin S = 1/2) ion in trigonal symmetry, respectively. According to the investigations, the nd⁵ (n = 3 and 4) impurity ions may not locate at the ideal Al³⁺ site but undergo axial displacements by about 0.132 Å and 0.170 Å for Fe³⁺ and Ru³⁺, respectively, away from the center of the ligand octahedron along the C₃ axis. The calculated spin Hamiltonian parameters based on the above axial displacements show good agreement with the observed values. The validity of the results is discussed.     

Dynamic critical exponent of a Bose system to O(1n)

The dynamic critical exponent of an n-component Bose system is calculated by the 1/n expansion technique to order 1/n in 2 < d < 4 dimensions.