Finite-temperature phase transitions in the quantum fully frustrated Ising models

The quantum antiferromagnetic spin-1/2 Ising model on a triangular lattice and analogous fully frustrated Ising model on a square lattice with quantum fluctuations induced by the application of the transverse magnetic field are studied at finite temperatures by constructing an exact mapping onto a purely classical model with a more complex interaction. It is shown that in weak fields the temperatures of the phase transitions separating the critical phase from the ordered and disordered phases in both models are proportional to the magnitude of the field.Comment: 5 pages, RevTex

Radiative Corrections to QCD Amplitudes in Quasi-Multi-Regge Kinematics

Radiative corrections to QCD amplitudes in the quasi-multi-Regge kinematics are interesting in particular since the Reggeized form of these amplitudes is used in the derivation of the NLO BFKL. This form is a hypothesis which must be at least carefully checked, if not proved. We calculate the radiative corrections in the one-loop approximation using the s-channel unitarity. Compatibility of the Reggeized form of the amplitudes with the s-channel unitarity requires fulfillment of the set of nonlinear equations for the Reggeon vertices. We show that these equations are satisfied.Comment: 28 pages,3 figure

Scaling, Finite Size Effects, and Crossovers of the Resistivity and Current-Voltage Characteristics in Two-Dimensional Superconductors

We revisit the scaling properties of the resistivity and the current-voltage characteristics at and below the Berezinskii-Kosterlitz-Thouless transition, both in zero and nonzero magnetic field. The scaling properties are derived by integrating the renormalization group flow equations up to a scale where they can be reliably matched to simple analytic expressions. The vortex fugacity turns out to be dangerously irrelevant for these quantities below Tc, thereby altering the scaling behavior. We derive the possible crossover effects as the current, magnetic field, or system size is varied, and find a strong multiplicative logarithmic correction near Tc, all of which is necessary to account for when interpreting experiments and simulation data. Our analysis clarifies a longstanding discrepancy between the finite size dependence found in many simulations and the current-voltage characteristics of experiments. We further show that the logarithmic correction can be avoided by approaching the transition in a magnetic field, thereby simplifying the scaling analysis. We confirm our results by large-scale numerical simulations, and calculate the dynamic critical exponent z, for relaxational Langevin dynamics and for resistively and capacitively shunted Josephson junction dynamics.Comment: 5 pages, 2 figure

To the modification of methods of nuclear chronometry in astrophysics and geophysics

In practically all known till now methods of nuclear chronometry there were usually taken into account the life-times of only fundamental states of $\alpha$-radioactive nuclei. But in the processes of nuclear synthesis in stars and under the influence of the constant cosmic radiation on surfaces of planets the excitations of the $\alpha$-radioactive nuclei are going on. Between them there are the states with the excited $\alpha$-particles inside the parent nuclei and so with much smaller life-times. And inside the large masses of stellar, terrestrial and meteoric substances the transitions between different internal conditions of radioactive nuclei are accompanied by infinite chains of the $\gamma$-radiations with the subsequent $\gamma$-absorptions, the further $\gamma$-radiations etc. For the description of the $\alpha$-decay evolution with considering of such excited states and multiple $\gamma$-radiations and $\gamma$-absorptions inside stars and under the influence of the cosmic radiation on the earth surface we present the quantum-mechanical approach, which is based on the generalized Krylov-Fock theorem. Some simple estimations are also presented. They bring to the conclusion that the usual (non-corrected) "nuclear clocks" do really indicate not to realistic values but to the \emph{upper limits} of the durations of the $\alpha$-decay stellar and planet processes.Comment: 6 pages, Standard LaTeX v.2

Dunajski generalization of the second heavenly equation: dressing method and the hierarchy

Dunajski generalization of the second heavenly equation is studied. A dressing scheme applicable to Dunajski equation is developed, an example of constructing solutions in terms of implicit functions is considered. Dunajski equation hierarchy is described, its Lax-Sato form is presented. Dunajsky equation hierarchy is characterized by conservation of three-dimensional volume form, in which a spectral variable is taken into account.Comment: 13 page

Role of quark-instanton liquid interactions in colour superconductivity phase

The interaction of light quarks and instanton liquid is analyzed at finite density of quark/baryon matter and in the phase of nonzero values of diquark (colour) condensate. It is shown that instanton liquid perturbation produced by such an interaction results in an essential increase of the critical value of quark chemical potential $\mu_c$ which provokes the perceptible increase of quark matter density around the expected onset of the colour superconductivity phase.Comment: 11 pages, 5 figure

Magnetocaloric effect and nature of magnetic transition in nanoscale Pr0.5Ca0.5MnO3

Systematic measurements pertinent to the magnetocaloric effect and nature of magnetic transition around the transition temperature are performed in the 10 nm Pr0.5Ca0.5MnO3 nanoparticles (PCMO10) . Maxwell relation is employed to estimate the change in magnetic entropy. At Curie temperature TC, 83.5 K, the change in magnetic entropy discloses a typical variation with a value 0.57 J/kg K, and is found to be magnetic field dependent. From the area under the curve Delta S vs T, the refrigeration capacity is calculated at TC, 83.5 K and it is found to be 7.01 J/kg. Arrott plots infer that due to the competition between the ferromagnetic and anti ferromagnetic interactions, the magnetic phase transition in PCMO10 is broadly spread over both in temperature as well as in magnetic field coordinates. Upon tuning the particle size, size distribution, morphology, and relative fraction of magnetic phases, it may be possible to enhance the magnetocalorific effect further in PCMO10.Comment: Accepted (Journal of Applied Physics) (In press

Photon-Reggeon Interaction Vertices in the Nla

We calculate the effective vertices for the quark-antiquark and the quark-antiquark-gluon production in the virtual photon - Reggeized gluon interaction. The last vertex is considered at the Born level; for the first one the one-loop corrections are obtained. These vertices have a number of applications; in particular, they are necessary for calculation of the virtual photon impact factor in the next-to-leading logarithmic approximation.Comment: 20 pages, references adde