Itinerant Ferromagnetism in the electronic localization limit

We present Hall effect, $R_{xy}(H)$, and magnetoresistance, $R_{xx}(H)$, measurements of ultrathin films of Ni, Co and Fe with thicknesses varying between 0.2-8 nm and resistances between 1 M$\Omega$ - 100 $\Omega.$ Both measurements show that films having resistance above a critical value, $R_{C}$, (thickness below a critical value, $d_{C}$) show no signs for ferromagnetism. Ferromagnetism appears only for films with $R<R_{C}$, where $R_{C}$ is material dependent. We raise the possibility that the reason for the absence of spontaneous magnetization is suppression of itinerant ferromagnetism by electronic disorder in the strong localization regime.Comment: 4 pages, 4 figure

Optical counterparts of cosmological GRBs due to heating of ISM in the parent galaxy

We investigated influence of cosmological GRB on the surrounding interstellar medium. It was shown that \gamma-radiation from the burst heats interstellar gas to the temperatures > 10^4 K up to the distance \sim 10 pc. For high density ISM optical and UV radiation of the heated gas can be observed on the Eath several years as a GRB`s counterpartComment: 2 pages, 1 figure; presented at the Rome Conference on Gamma Ray Bursts in the Afterglow Ag

Reply to [arXiv:1201.5347] "Comment on 'Vortex-assisted photon counts and their magnetic field dependence in single-photon superconducting detectors'"

We argue that cutoff in the London model cannot be settled without use of the microscopic theory

Area Law and Continuum Limit in "Induced QCD"

We investigate a class of operators with non-vanishing averages in a D-dimensional matrix model recently proposed by Kazakov and Migdal. Among the operators considered are ``filled Wilson loops" which are the most reasonable counterparts of Wilson loops in the conventional Wilson formulation of lattice QCD. The averages of interest are represented as partition functions of certain 2-dimensional statistical systems with nearest neighbor interactions. The ``string tension" $\alpha'$, which is the exponent in the area law for the ``filled Wilson loop" is equal to the free energy density of the corresponding statistical system. The continuum limit of the Kazakov--Migdal model corresponds to the critical point of this statistical system. We argue that in the large $N$ limit this critical point occurs at zero temperature. In this case we express $\alpha'$ in terms of the distribution density of eigenvalues of the matrix-valued master field. We show that the properties of the continuum limit and the description of how this limit is approached is very unusual and differs drastically from what occurs in both the Wilson theory ($S\propto({\rm Tr}\prod U +{\rm c.c.})$) and in the ``adjoint'' theory ($S\propto\vert{\rm Tr}\prod U\vert^2$). Instead, the continuum limit of the model appears to be intriguingly similar to a $c>1$ string theory.Comment: 38 page

Continuum Limits of ``Induced QCD": Lessons of the Gaussian Model at d=1 and Beyond

We analyze the scalar field sector of the Kazakov--Migdal model of induced QCD. We present a detailed description of the simplest one dimensional {($d$$=$$1$)} model which supports the hypothesis of wide applicability of the mean--field approximation for the scalar fields and the existence of critical behaviour in the model when the scalar action is Gaussian. Despite the ocurrence of various non--trivial types of critical behaviour in the $d=1$ model as $N\rightarrow\infty$, only the conventional large-$N$ limit is relevant for its {\it continuum} limit. We also give a mean--field analysis of the $N=2$ model in {\it any} $d$ and show that a saddle point always exists in the region $m^2>m_{\rm crit}^2(=d)$. In $d=1$ it exhibits critical behaviour as $m^2\rightarrow m_{\rm crit}^2$. However when $d$$>$$1$ there is no critical behaviour unless non--Gaussian terms are added to the scalar field action. We argue that similar behaviour should occur for any finite $N$ thus providing a simple explanation of a recent result of D. Gross. We show that critical behaviour at $d$$>$$1$ and $m^2>m^2_{\rm crit}$ can be obtained by adding a $logarithmic$ term to the scalar potential. This is equivalent to a local modification of the integration measure in the original Kazakov--Migdal model. Experience from previous studies of the Generalized Kontsevich Model implies that, unlike the inclusion of higher powers in the potential, this minor modification should not substantially alter the behaviour of the Gaussian model.Comment: 31 page