12 research outputs found
Hall Conductivity for Two Dimensional Magnetic Systems
A Kubo inspired formalism is proposed to compute the longitudinal and
transverse dynamical conductivities of an electron in a plane (or a gas of
electrons at zero temperature) coupled to the potential vector of an external
local magnetic field, with the additional coupling of the spin degree of
freedom of the electron to the local magnetic field (Pauli Hamiltonian). As an
example, the homogeneous magnetic field Hall conductivity is rederived. The
case of the vortex at the origin is worked out in detail. This system happens
to display a transverse Hall conductivity ( breaking effect) which is
subleading in volume compared to the homogeneous field case, but diverging at
small frequency like . A perturbative analysis is proposed for the
conductivity in the random magnetic impurity problem (Poissonian vortices in
the plane). At first order in perturbation theory, the Hall conductivity
displays oscillations close to the classical straight line conductivity of the
mean magnetic field.Comment: 28 pages, latex, 2 figure
Geometric Exponents, SLE and Logarithmic Minimal Models
In statistical mechanics, observables are usually related to local degrees of
freedom such as the Q < 4 distinct states of the Q-state Potts models or the
heights of the restricted solid-on-solid models. In the continuum scaling
limit, these models are described by rational conformal field theories, namely
the minimal models M(p,p') for suitable p, p'. More generally, as in stochastic
Loewner evolution (SLE_kappa), one can consider observables related to nonlocal
degrees of freedom such as paths or boundaries of clusters. This leads to
fractal dimensions or geometric exponents related to values of conformal
dimensions not found among the finite sets of values allowed by the rational
minimal models. Working in the context of a loop gas with loop fugacity beta =
-2 cos(4 pi/kappa), we use Monte Carlo simulations to measure the fractal
dimensions of various geometric objects such as paths and the generalizations
of cluster mass, cluster hull, external perimeter and red bonds. Specializing
to the case where the SLE parameter kappa = 4p'/p is rational with p < p', we
argue that the geometric exponents are related to conformal dimensions found in
the infinitely extended Kac tables of the logarithmic minimal models LM(p,p').
These theories describe lattice systems with nonlocal degrees of freedom. We
present results for critical dense polymers LM(1,2), critical percolation
LM(2,3), the logarithmic Ising model LM(3,4), the logarithmic tricritical Ising
model LM(4,5) as well as LM(3,5). Our results are compared with rigourous
results from SLE_kappa, with predictions from theoretical physics and with
other numerical experiments. Throughout, we emphasize the relationships between
SLE_kappa, geometric exponents and the conformal dimensions of the underlying
CFTs.Comment: Added reference
Density correlations of magnetic impurities and disorder
We consider an electron coupled to a random distribution of point vortices in the plane (magnetic impurities). We analyze the effect of the magnetic impurities on the density of states of the test particle, when the magnetic impurities have a spatial probability distribution governed by Bose or Fermi statistic at a given temperature. Comparison is made with the Poisson distribution, showing that the zero temperature Fermi distribution corresponds to less disorder. A phase diagram describing isolated impurities versus Landau level oscillations is proposed
Anyonic partition functions and windings of planar Brownian motion
The computation of the -cycle brownian paths contribution to
the -anyon partition function is adressed. A detailed numerical analysis
based on random walk on a lattice indicates that . In the paramount -anyon case, one
can show that is built by linear states belonging to the bosonic,
fermionic, and mixed representations of .Comment: 11 pages + 1 figure upon reques
Magnetic fields and brownian motion on the 2-sphere
Virginia BlĂźnda Institut for East European Studies Romanian Academy Searching an identity: the destiny of the print censured in Moldavia - (1832-1862
Magnetic fields and brownian motion on the 2-sphere
Virginia BlĂźnda Institut for East European Studies Romanian Academy Searching an identity: the destiny of the print censured in Moldavia - (1832-1862