On the theory of phase transition in muliferroics

In this paper we investigate peculiarities of phase transition high-symmetry - incommensurate phase in inhomogeneous systems. We obtain the nonlinear dispersion law and then present a renormalization group analysis of phase transitions in multiferroics. We have determined the dependence of critical indices on the nonextensivity parameter of the system

Percolation in high dimensions is not understood

The number of spanning clusters in four to nine dimensions does not fully follow the expected size dependence for random percolation.Comment: 9-dimensional data and more points for large lattices added; statistics improved, text expanded, table of exponents inserte

Stable Non-Supersymmetric Supergravity Solutions from Deformations of the Maldacena-Nunez Background

We study a deformation of the type IIB Maldacena-Nunez background which arises as the near-horizon limit of NS5 branes wrapped on a two-cycle. This background is dual to a "little string theory" compactified on a two-sphere, a theory which at low energies includes four-dimensional N = 1 super Yang-Mills theory. The deformation we study corresponds to a mass term for some of the scalar fields in this theory, and it breaks supersymmetry completely. In the language of seven-dimensional SO(4) gauged supergravity the deformation involves (at leading order) giving a VEV, depending only on the radial coordinate, to a particular scalar field. We explicitly construct the corresponding solution at leading order in the deformation, both in seven-dimensional and in ten-dimensional supergravity, and we verify that it completely breaks supersymmetry. Since the original background had a mass gap and we are performing a small deformation, the deformed background is guaranteed to be stable even though it is not supersymmetric.Comment: 1+31 pages, one figure. v2: minor clarifications, refs adde

Two-dimensional Site-Bond Percolation as an Example of Self-Averaging System

The Harris-Aharony criterion for a statistical model predicts, that if a specific heat exponent $\alpha \ge 0$, then this model does not exhibit self-averaging. In two-dimensional percolation model the index $\alpha=-{1/2}$. It means that, in accordance with the Harris-Aharony criterion, the model can exhibit self-averaging properties. We study numerically the relative variances $R_{M}$ and $R_{\chi}$ for the probability $M$ of a site belongin to the "infinite" (maximum) cluster and the mean finite cluster size $\chi$. It was shown, that two-dimensional site-bound percolation on the square lattice, where the bonds play the role of impurity and the sites play the role of the statistical ensemble, over which the averaging is performed, exhibits self-averaging properties.Comment: 15 pages, 5 figure

Breakdown of `phase rigidity' and variations of the Fano effect in closed Aharonov-Bohm interferometers

Although the conductance of a closed Aharonov-Bohm interferometer, with a quantum dot on one branch, obeys the Onsager symmetry under magnetic field reversal, it needs not be a periodic function of this field: the conductance maxima move with both the field and the gate voltage on the dot, in an apparent breakdown of `phase rigidity'. These experimental findings are explained theoretically as resulting from multiple electronic paths around the interferometer ring. Data containing several Coulomb blockade peaks, whose shapes change with the magnetic flux, are fitted to a simple model, in which each resonant level on the dot couples to a different path around the ring

A Note on Softly Broken MQCD

We consider generic MQCD configurations with matter described by semi-infinte D4-branes and softly broken supersymmetry. We show that the matter sector does not introduce supersymmetry breaking parameters so that the most relevant supersymmetry breaking operator at low energies is the gaugino mass term. By studying the run-away properties of these models in the decoupling limit of the adjoint matter, we argue that these softly broken MQCD configurations fail to capture the infrared physics of QCD at scales below the gaugino mass scale.Comment: 10+1 pages, TeX. V2: small comments and acknowledgements added, conclusions unchange