Statistical Derivation of Basic Equations of Diffusional Kinetics in Alloys with Application to the Description of Diffusion of Carbon in Austenite

Basic equations of diffusional kinetics in alloys are statistically derived using the master equation approach. To describe diffusional transformations in substitution alloys, we derive the "quasi-equilibrium" kinetic equation which generalizes its earlier versions by taking into account possible "interaction renormalization" effects. For the interstitial alloys Me-X, we derive the explicit expression for the diffusivity D of an interstitial atom X which notably differs from those used in previous phenomenological treatments. This microscopic expression for D is applied to describe the diffusion of carbon in austenite basing on some simple models of carbon-carbon interaction. The results obtained enable us to make certain conclusions about the real form of these interactions, and about the scale of the "transition state entropy" for diffusion of carbon in austenite.Comment: 26 pages, 5 postscript figures, LaTe

Role of Disorder in Mn:GaAs, Cr:GaAs, and Cr:GaN

We present calculations of magnetic exchange interactions and critical temperature T_c in Mn:GaAs, Cr:GaAs and Cr:GaN. The local spin density approximation is combined with a linear-response technique to map the magnetic energy onto a Heisenberg hamiltonion, but no significant further approximations are made. Special quasi-random structures in large unit cells are used to accurately model the disorder. T_c is computed using both a spin-dynamics approach and the cluster variation method developed for the classical Heisenberg model. We show the following: (i) configurational disorder results in large dispersions in the pairwise exchange interactions; (ii) the disorder strongly reduces T_c; (iii) clustering in the magnetic atoms, whose tendency is predicted from total-energy considerations, further reduces T_c. Additionally the exchange interactions J(R) are found to decay exponentially with distance R^3 on average; and the mean-field approximation is found to be a very poor predictor of T_c, particularly when J(R) decays rapidly. Finally the effect of spin-orbit coupling on T_c is considered. With all these factors taken into account, T_c is reasonably predicted by the local spin-density approximation in MnGaAs without the need to invoke compensation by donor impurities.Comment: 10 pages, 3 figure

Spin ice in a field: quasi-phases and pseudo-transitions

Thermodynamics of the short-range model of spin ice magnets in a field is considered in the Bethe - Peierls approximation. The results obtained for [111], [100] and [011] fields agrees reasonably well with the existing Monte-Carlo simulations and some experiments. In this approximation all extremely sharp field-induced anomalies are described by the analytical functions of temperature and applied field. In spite of the absence of true phase transitions the analysis of the entropy and specific heat reliefs over H-T plane allows to discern the "pseudo-phases" with specific character of spin fluctuations and define the lines of more or less sharp "pseudo-transitions" between them.Comment: 18 pages, 16 figure

Semi-fermionic representation for spin systems under equilibrium and non-equilibrium conditions

We present a general derivation of semi-fermionic representation for spin operators in terms of a bilinear combination of fermions in real and imaginary time formalisms. The constraint on fermionic occupation numbers is fulfilled by means of imaginary Lagrange multipliers resulting in special shape of quasiparticle distribution functions. We show how Schwinger-Keldysh technique for spin operators is constructed with the help of semi-fermions. We demonstrate how the idea of semi-fermionic representation might be extended to the groups possessing dynamic symmetries (e.g. singlet/triplet transitions in quantum dots). We illustrate the application of semi-fermionic representations for various problems of strongly correlated and mesoscopic physics.Comment: Review article, 40 pages, 11 figure

Single Electron Spin Decoherence by Nuclear Spin Bath: Linked Cluster Expansion Approach

We develop a theoretical model for transverse dynamics of a single electron spin interacting with a nuclear spin bath. The approach allows a simple diagrammatic representation and analytical expressions of different nuclear spin excitation processes contributing to electron spin decoherence and dynamical phase fluctuations. It accounts for nuclear spin dynamics beyond conventional pair correlation models. As an illustration of the theory, we evaluated the coherence dynamics of a P donor electron spin in a Si crystal.Comment: 37 pages, 13 figure

Symmetries and Ambiguities in the linear sigma model with light quarks

We investigate the role of undetermined finite contributions generated by radiative corrections in a $SU(2)\times SU(2)$ linear sigma model with quarks. Although some of such terms can be absorbed in the renormalization procedure, one such contribution is left in the expression for the pion decay constant. This arbitrariness is eliminated by chiral symmetry.Comment: 9 pages. Added references through the text; an author was added due to an important contribution; corrected typos; the title also was changed. Submitted to Modern Physics Letter

Anharmonicity of BaTiO_3 single crystals

By analyzing the dielectric non-linearity with the Landau thermodynamic expansion, we find a simple and direct way to assess the importance of the eighth order term. Following this approach, it is demonstrated that the eighth order term is essential for the adequate description of the para/ferroelectric phase transition of BaTiO_3. The temperature dependence of the quartic coefficient \beta is accordingly reconsidered and is strongly evidenced by the change of its sign above 165 C. All these findings attest to the strong polarization anharmonicity of this material, which is unexpected for classical displacive ferroelectrics.Comment: 4 figures, to be published in Phys. Rev.

Loop series for discrete statistical models on graphs

In this paper we present derivation details, logic, and motivation for the loop calculus introduced in \cite{06CCa}. Generating functions for three inter-related discrete statistical models are each expressed in terms of a finite series. The first term in the series corresponds to the Bethe-Peierls (Belief Propagation)-BP contribution, the other terms are labeled by loops on the factor graph. All loop contributions are simple rational functions of spin correlation functions calculated within the BP approach. We discuss two alternative derivations of the loop series. One approach implements a set of local auxiliary integrations over continuous fields with the BP contribution corresponding to an integrand saddle-point value. The integrals are replaced by sums in the complimentary approach, briefly explained in \cite{06CCa}. A local gauge symmetry transformation that clarifies an important invariant feature of the BP solution, is revealed in both approaches. The partition function remains invariant while individual terms change under the gauge transformation. The requirement for all individual terms to be non-zero only for closed loops in the factor graph (as opposed to paths with loose ends) is equivalent to fixing the first term in the series to be exactly equal to the BP contribution. Further applications of the loop calculus to problems in statistical physics, computer and information sciences are discussed.Comment: 20 pages, 3 figure

New phase structure of the Nambu -- Jona - Lasinio model at nonzero chemical potential

It is shown that in the Nambu -- Jona - Lasinio model at nonzero chemical potential there are two different massive phases with spontaneously broken chiral symmetry. In one of them particle density is identically zero, in another phase it is not equal to zero. The transition between phases is a phase transition of the second order.Comment: 8 pages, LaTeX, no figures