A Green-function theory for the dynamic spin susceptibility in the square-lattice spin-1/2 antiferromagnetic compass-Heisenberg model employing a generalized mean-field approximation is presented. The theory describes magnetic long-range order (LRO) and short-range order (SRO) at arbitrary temperatures. The magnetization, Neel temperature T_N, specific heat, and uniform static spin susceptibility $chi$ are calculated self-consistently. As the main result, we obtain LRO at finite temperatures in two dimensions, where the dependence of T_N on the compass-model interaction is studied. We find that T_N is close to the experimental value for Ba2IrO4. The effects of SRO are discussed in relation to the temperature dependence of $chi$.
A detailed description of the method for analytical evaluation of the three-loop contributions to renormalization group functions is presented. This method is employed to calculate the charge renormalization function and anomalous dimensions for non-Abelian gauge theories with fermions in the three-loop approximation. A three-loop expression for the effective charge of QCD is given. Charge renormalization effects in the SU(4)-supersymmetric gauge model is shown to vanish at this level. A complete list of required formulas is given in Appendix. The above-mentioned results of three-loop calculations have been published by the present authors (with A.Yu., Zharkov and L.V., Avdeev) in 1980 in Physics Letters B. The present text, which treats the subject in more details and contains a lot of calculational techniques, has also been published in 1980 as the JINR Communication E2-80-483.
We consider integrals $tau_{rho}=int_0^1rhoxi^2,dx$, where $xi$ is Wiener process and $rho$ is generalized function from some class of multipliers. In the case when multiplier $rho$ belongs to the trace-class, it is shown that $tau_{rho}$ has $chi^2$-distribution (or analogous). An example of multiplier $rho$ not belonging to the trace-class is constructed.
Sturm-Liouville spectral problem for equation $-(y/r)+qy=lambda py$ with generalized functions $rge 0$, $q$ and $p$ is considered. It is shown that the problem may be reduced to analogous problem with $requiv 1$. The case of $q=0$ and self-similar $r$ and $p$ is considered as an example.
On the basis of the theory of Sturm--Liouville problem with distribution coefficients we get the infima and suprema of the first eigenvalue of the problem $-y + (q-lambda) y=0, y(0) -k_0^2 y(0) = y(1) + k_1^2 y(1) = 0$, where $q$ belongs to the set of constant-sign summable functions on $[0,1]$ such that $int_0^1 q dx=pm 1$.
A microscopic theory of the electrical conductivity $sigma(omega)$ within the t-J model is developed. An exact representation for $sigma(omega)$ is obtained using the memory-function technique for the relaxation function in terms of the Hubbard operators, and the generalized Drude law is derived. The relaxation rate due to the decay of charge excitations into particle-hole pairs assisted by antiferromagnetic spin fluctuations is calculated in the mode-coupling approximation. Using results for the spectral function of spin excitations calculated previously, the relaxation rate and the optical and dc conductivities are calculated in a broad region of doping and temperatures. The reasonable agreement of the theory with experimental data for cuprates proves the important role of spin-fluctuation scattering in the charge dynamics.
The present paper deals with the spectral and the oscillation properties of a linear pencil $A-lambda B$. Here $A$ and $B$ are linear operators generated by the differential expressions $(py)$ and $-y+ cry$, respectively. In particular, it is shown that the negative eigenvalues of this problem are simple and the corresponding eigenfunctions $y_{-n}$ have $n-1$ zeros in $(0,1)$.
Self-adjoint boundary problems for the equation $y^{(4)}-lambdarho y=0$ with generalized derivative $rhoin W_2^{-1}[0,1]$ of self-similar Cantor type function as a weight are considered. Using the oscillating properties of the eigenfunctions, the spectral asymptotics are made more precise then in previous papers.
