1,627,329 research outputs found
Critical behavior of an Ising model with aperiodic interactions
We write exact renormalization-group recursion relations for a ferromagnetic
Ising model on the diamond hierarchical lattice with an aperiodic distribution
of exchange interactions according to a class of generalized two-letter
Fibonacci sequences. For small geometric fluctuations, the critical behavior is
unchanged with respect to the uniform case. For large fluctuations, the uniform
fixed point in the parameter space becomes fully unstable. We analyze some
limiting cases, and propose a heuristic criterion to check the relevance of the
fluctuations.Comment: latex file, 5 figures, accepted by Braz. Jour. Phy
Charged spin 1/2 particle in an arbitrary magnetic field in two spatial dimensions: a supersymmetric quantum mechanical system
It is shown that the 2 X 2 matrix Hamiltonian describing the dynamics of a
charged spin 1/2 particle with g-factor 2 moving in an arbitrary, spatially
dependent, magnetic field in two spatial dimensions can be written as the
anticommuator of a nilpotent operator and its hermitian conjugate.
Consequently, the Hamiltonians for the two different spin projections form
partners of a supersymmetric quantum mechanical system. The resulting
supersymmetry algebra can then be exploited to explicitly construct the exact
zero energy ground state wavefunction for the system. Modulo this ground state,
the remainder of the eigenstates and eigenvalues of the two partner
Hamiltonians form positive energy degenerate pairs. We also construct the
spatially asymptotic form of the magnetic field which produces a finite
magnetic flux and associated zero energy normalizable ground state
wavefunction.Comment: 10 pages, LaTe
Flows on Graphs with Random Capacities
We investigate flows on graphs whose links have random capacities. For binary
trees we derive the probability distribution for the maximal flow from the root
to a leaf, and show that for infinite trees it vanishes beyond a certain
threshold that depends on the distribution of capacities. We then examine the
maximal total flux from the root to the leaves. Our methods generalize to
simple graphs with loops, e.g., to hierarchical lattices and to complete
graphs.Comment: 8 pages, 6 figure
Temperature-driven transition from the Wigner Crystal to the Bond-Charge-Density Wave in the Quasi-One-Dimensional Quarter-Filled band
It is known that within the interacting electron model Hamiltonian for the
one-dimensional 1/4-filled band, the singlet ground state is a Wigner crystal
only if the nearest neighbor electron-electron repulsion is larger than a
critical value. We show that this critical nearest neighbor Coulomb interaction
is different for each spin subspace, with the critical value decreasing with
increasing spin. As a consequence, with the lowering of temperature, there can
occur a transition from a Wigner crystal charge-ordered state to a spin-Peierls
state that is a Bond-Charge-Density Wave with charge occupancies different from
the Wigner crystal. This transition is possible because spin excitations from
the spin-Peierls state in the 1/4-filled band are necessarily accompanied by
changes in site charge densities. We apply our theory to the 1/4-filled band
quasi-one-dimensional organic charge-transfer solids in general and to 2:1
tetramethyltetrathiafulvalene (TMTTF) and tetramethyltetraselenafulvalene
(TMTSF) cationic salts in particular. We believe that many recent experiments
strongly indicate the Wigner crystal to Bond-Charge-Density Wave transition in
several members of the TMTTF family. We explain the occurrence of two different
antiferromagnetic phases but a single spin-Peierls state in the generic phase
diagram for the 2:1 cationic solids. The antiferromagnetic phases can have
either the Wigner crystal or the Bond-Charge-Spin-Density Wave charge
occupancies. The spin-Peierls state is always a Bond-Charge-Density Wave.Comment: 12 pages, 8 EPS figures. Longer version of previous manuscript.
Contains new numerical data as well as greatly expanded discussio
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