Systems with separable many-particle interactions. I

In this paper we give an exact evaluation of the free energy per particle for systems with separable many-particle interactions described by a hamiltonian of the type ? = ∑_kT(k) + NP (N^-1 ∑_kV(k)), where P is an arbitrary polynomial. In the proof use is made of a fundamental theorem due to Bogoliubov Jr. for ferromagnetic quadratic operators. The free energy can be obtained from a trial hamiltonian, which is linear in the operators T and V.     

Convex-envelope formulation for separable many-particle interactions

The exact result for the free energy per particle in systems described by a hamiltonian of the type NP(V_N), where NV_N denotes a set of short-range operators, is reformulated in terms of a convex-envelope construction. A comparison is given with results obtained for classical systems with interactions of the so-called Kac-type.     

Systems with separable many-particle interactions. II

The treatment of a previous paper on systems with many-particle interactions is generalized to hamiltonians containing an analytic function of a number of short-range interaction operators V, which are normalized. An exact expression for the free energy per particle in the thermodynamic limit can be obtained from a trial hamiltonian which is linear in the operators V.     

The temperature-dependent phase diagrams of the spin-3/2 Ising model on a FM/AFM two-layer lattice with a crystal field

The temperature-dependent phase diagrams of the spin-3/2 Ising model on a two-layer Bethe lattice with ferromagnetic (FM)/antiferromagnetic (AFM) intra-layer and either FM or AFM type inter-layer interactions are investigated under a constant magnetic field (H) and in the presence of a crystal field (D) by using exact recursion equations in a pairwise approach for coordination numbers q=3,4 and 6, in detail. In the light of the ground-state (GS) phase diagrams, the temperature-dependent phase diagrams of the model are obtained by studying the thermal variations of the order parameters, response functions and free energy. Then, they are illustrated on the (kT/J₁,J₃/J₁) and (kT/J₁,J₂/J₁) planes for the given system parameters. It is observed that the system exhibits first- and second-order phase transitions for all q values, and hence, in some cases, tricritical points. The existence of critical-end points and that of isolated points are also observed. The re-entrant behavior owes its presence to the two Néel temperatures, T_N, that are present for all q.     

Critical temperature for a system with Heisenberg-like nearest neighbour and Ising-like next nearest neighbour interactions

A ferromagnetic system with $\text{S =}\text{1}\text{2}$, where the interactions between nearest neighbours are isotropic (having Heisenberg character) and those between the next nearest neighbours anisotropic (Ising-like), is investigated. Using the effective hamiltonian approach we find the change in the critical temperature due to the inclusion of next nearest neighbour interactions of different character. The change is greatest in two dimensions where the critical temperature is shifted up from its zero value for a system with the Ising-like interactions switched off. We also calculate the T_c for a system with both nearest and next nearest neighbours interactions of the Ising-type. The results for the two models are compared.     

Spin-pair correlations of the classical Heisenberg ferromagnet above and below the critical point: Results of self-consistent Monte Carlo calculations

The spin-pair correlation functions of the classical Heisenberg ferromagnet with simple cubic lattice have been calculated in the paramagnetic and ferromagnetic temperature range using the self-consistent Monte Carlo method. The results agree with high-temperature series expansions aboveT _c , for low temperatures with spin-wave theory. By two different approaches the divergence of the ferromagnetic homogeneous susceptibility in zero field throughout the ferromagnetic temperature range could be verified. The functional dependence of the static susceptibilityχ _T (k) upon the inverse correlation lengthκ ₁ is discussed above and belowT _c and a Fourier transform for the explicit dependence of the spin correlations upon correlation length belowT _c is given. According to these results the scaling assumptionv=v′ for the exponents of the correlation length in the critical region is consistent with a divergent ferromagnetic susceptibility.     

Strong short range magnetic order in ferromagnetic transition metals above Tc: A theoretical explanation

A theory for the existence of strong short range magnetic order in itinerant magnetism above T_c is presented. We derive a characteristic lengthscale for short range order, given by the square root of bandwidth over k_BT_c. This is of order 20 Å in the ferromagnetic transition metals.     

Remark on the application of the effective hamiltonian method for random systems

We compare two versions of the effective Hamiltonian method applied to random bond systems. In one randomness is treated in a kind of the mean field approximation, whereas in the other the relevant arrangements of bonds are explicitly accounted for. Calculations for three dimensional systems of mixed ferromagnetic Heisenberg and Ising bonds show that although the T_c vs p (concentration of Heisenberg-loke interactions) curve in the second approach lies closer to the results of high temperature series general features in both approxsimations are quite similar.     

Quenching of ππ* triplet states of vaporous polycyclic aromatic compounds by oxygen

The oxygen quenching rate constants k _T ^O2 of the triplet state T ₁ of vapors of polycyclic aromatic hydrocarbons (PAHs) with strongly different oxidation potentials 0.44 eV < E _OX < 1.61 eV and energies of the triplet levels 14800 cm^?1 < E _T < 24500 cm^?1 (anthracene, 2-aminoanthracene, 9-nitroanthracene, chrysene, phenanthrene, fluoranthene, and carbazole) are estimated from the measured dependences of the decay rates and intensities of delayed fluorescence on the oxygen pressure P _O2. It is found that the rate constants k _T ^O2 vary from 4 × 10³ (9-nitroanthracene) to 4 × 10⁵ s^?1 Torr^?1 (2-aminoanthracene) and increase with decreasing oxidation potentials E _OX of PAHs. The rate constants k _T ^O2 for vapors and solutions are compared. The dependences of k _T ^O2 on the free energy of two intermolecular processes, namely, triplet energy transfer to oxygen and electron transfer, are analyzed. It is shown that the rate constants k _T ^O2 increase with decreasing electron transfer free energy, which proves that, along with energy transfer, charge-transfer interactions contribute to the quenching of the triplet states of PAH vapors.     

Bound ferromagnetic and paramagnetic polarons as an origin of the resistivity peak in ferromagnetic semiconductors and manganites

A theory of resistivity is developed for ferromagnetic semiconductors, possibly, including manganites. The theory is based on analysis of the interaction of the free and bound charge carriers with the magnetization of the crystal. The temperature dependence of free energy for nonionized donors and free electrons is calculated for the spin-wave and paramagnetic regions. In addition to the trapping by the ferromagnetic fluctuations (the ferromagnetic polarons), the electron trapping by the random magnetization fluctuations as T → is taken into account (the paramagnetic polarons). For the nondegenerate semiconductors, the theory makes it possible to explain a nonmonotonic temperature dependence of the activation energy, with the value for T = 0 being lower than that for T → ∞. For degenerate semiconductors, the theory explains a metal-insulator transition that occurs with increasing temperature in samples with relatively low charge carrier density. If the density is larger, a reentrant metal-insulator transition should take place, so that the crystal is highly conductive as T → ∞.     

Survival of Virus Particles in Water Droplets: Hydrophobic Forces and Landauer’s Principle

Many small biological objects, such as viruses, survive in a water environment and cannot remain active in dry air without condensation of water vapor. From a physical point of view, these objects belong to the mesoscale, where small thermal fluctuations with the characteristic kinetic energy of k_BT (where k_B is the Boltzmann’s constant and T is the absolute temperature) play a significant role. The self-assembly of viruses, including protein folding and the formation of a protein capsid and lipid bilayer membrane, is controlled by hydrophobic forces (i.e., the repulsing forces between hydrophobic particles and regions of molecules) in a water environment. Hydrophobic forces are entropic, and they are driven by a system’s tendency to attain the maximum disordered state. On the other hand, in information systems, entropic forces are responsible for erasing information, if the energy barrier between two states of a switch is on the order of k_BT, which is referred to as Landauer’s principle. We treated hydrophobic interactions responsible for the self-assembly of viruses as an information-processing mechanism. We further showed a similarity of these submicron-scale processes with the self-assembly in colloidal crystals, droplet clusters, and liquid marbles.     

Re-entry in ferromagnetic superconductors

The re-entry phenomenon in magnetic superconductors is studied using the generalized Ginzburg-Landau free energy introduced by Blount and Varma. The re-entry temperature T_c2 is simply that temperature at which the magnetization acts as a source of induction strong enough to destroy superconductivity. Above T_c2 ferromagnetism and superconductivity coexist. The structure is an Abrikosov vortex lattice, with ferromagnetic magnetization spreading widely around the vortex cores. Within our approximations, the phase transition at T_c2 is of second order.     

Computational materials design of filled tetrahedral compound magnetic semiconductors

Based on first-principles calculations within the density functional theory, materials design of filled tetrahedral compound magnetic semiconductors is proposed. By using the Korringa–Kohn–Rostoker coherent potential approximation, electronic structures of Mn-doped LiZnAs, LiZnP and LiZnN are calculated. First, by estimating free energy, phase diagrams of these systems are predicted. It is shown that these systems are phase separating systems and favor spinodal decomposition. However, by introducing Li vacancies, spinodal decomposition is strongly suppressed and Mn can be doped up to high concentration. Moreover, the introduced Li vacancies induce ferromagnetic interaction between Mn and thus we can expect high Curie temperature (T_C) in these systems. To see the chemical trend, electronic structure and T_C of Li(Zn, Cr)As are also calculated.     

Simplified closed form expressions for irreducible tensor operators

A general closed form expression is derived which enables one to write a spherical tensor of rank L and projection k, T_uk^L, in terms of the familiar angular momentum operators, S_z and S². The simplicity of this expression results from an intriguing relationship between these spherical tensor operators (diagonal operator equivalents) and successive derivatives of Tchebichef orthogonal polynomials.     

Hexagonal spin structure of A-phase in MnSi: Densely packed skyrmion quasiparticles or two-dimensionally modulated spin superlattice?

We have studied in detail the A-phase region in the field-temperature (H-T) phase diagram of the cubic heli-magnet MnSi using small angle neutron diffraction. The A-phase revealed itself as a two-dimensional hexagonal pattern of Bragg spots with k _{h(1, 2, 3)} ⊥ H. The directions and magnitudes of the wave vectors k _{h(1, 2, 3)} are well preserved over the whole crystal of the size of 100 mm³, but in the small room of the (H-T) phase diagram just below T _c = 29 K. The droplets of the orientationally disordered, presumably hexagonal, spin structure with k _h ⊥ H are observed in the wide range beyond the A-phase boundaries in the field range from B _T1 ≈ 0.1 T to B _T2 ≈ 0.25 T at temperatures down to 15 K. No melting of these droplets into individual randomly located skyrmions is observed for all temperatures and magnetic fields. The wave vector of two-dimensional modulations k _h is equal to the wave vector of the cone phase k _c . We conclude that observable is a two dimensionally modulated hexagonal spin superlattice built on the same competition of interactions (ferromagnetic exchange and Dzyaloshinskii-Moriya interactions) similar to a case of one-dimensionally modulated simple spin spiral.     

Coherent state and superconductivity in the free carrier-bipolaron interacting system

In this paper a model to describe the free carrier-bipolaron interacting system is proposed. Effective hopping of the bipolaron is studied in the slave-boson approach, and a characteristic temperature T¹ is obtained, below which the system enters a coherent state. The density of states in the normal state and the superconductivity of the system are discussed in a quasiparticle picture. The results show that the mixing between the free carrier and the bipolaron results in an enhancement of the effective mass of the quasiparticle and meanwhile the renormalized coupling interaction, arising from the negative correlation energy in the bipolaron region, enhances the effective superconducting coupling interaction. Under the most favourable conditions, the superconducting transition temperature T_c ∼ ω_c, where ω_c is the Debye frequency related with local electron-phonon coupling. In general we have T¹ > T_c ⪢ T_c0 (T_c0 is the superconducting transition temperature of a usual superconductor). Therefore the system will firstly enter a coherent state before becoming a high-T_c superconductor.     

Incoherent tunneling at weak bias: Strong quantum damping

Using a generalized version of Langer's “imaginary part of the free energy” method involving an “extended” bounce and doing a fully “dynamical” evaluation of the weak bias anomalous fluctuation mode, the thermal dependence of the decay rate Γ = A exp(-B) is studied for a metastable quartic potential model in the strong ohmic quantum damping regime in order to extend previous work to a considerably more realistic range of parameters. In particular, the earlier restrictions 12 B exp(-ħω₀/2k_BT)→0 and 2πk_BT/ħω₀→0 are removed. As a consequence there appear - inter alia - T² -corrections in B similar to those occuring for strongly biased metastable systems.     

Longitudinal magnetoresistance in the Extreme Quantum Limit in nonparabolic semiconductors

We calculate the Longitudinal Magnetoresistance in the Extreme Quantum Limit (?Ω_c ? k_BT) for a nondegenerate n-type InSb sample at low temperatures when the dominant energy and momentum loss mechanisms are the el-acoustic phonon and the el-ionized impurity interactions. The magnetic field dependence of the effective mass which is due to the nonparabolic nature of the conduction band as well as the energy and magnetic field dependence of the relaxation time are incorporated in the analysis. Analytical results are presented for both nondegenerate and degenerate samples when individual scattering mechanisms are operative. In general nonparabolicity causes an enhancement in the Longitudinal Magnetoresistance and changes the nature of its magnetic field dependence as compared to the case of a parabolic conduction band.     

The mass gap for theP(φ)2 quantum field model with a strong external field

We consider theP(φ)₂ hamiltonian whose interaction density is given by $$\lambda P(\phi (x)) + \mu \phi (x)^k $$ wherek is odd and 1≦kP. For sufficiently large μ we show that there is a gap in the energy spectrum. In addition we obtain new regions of analyticity in λ and μ for the Schwinger functions and the pressure.