14,112 research outputs found
Spin-glass behaviour on random lattices
The ground-state phase diagram of an Ising spin-glass model on a random graph
with an arbitrary fraction of ferromagnetic interactions is analysed in the
presence of an external field. Using the replica method, and performing an
analysis of stability of the replica-symmetric solution, it is shown that
, correponding to an unbiased spin glass, is a singular point in the
phase diagram, separating a region with a spin-glass phase () from a
region with spin-glass, ferromagnetic, mixed, and paramagnetic phases
()
Replica-symmetric solutions of a dilute Ising ferromagnet in a random field
We use the replica method in order to obtain an expression for the
variational free energy of an Ising ferromagnet on a Viana-Bray lattice in the
presence of random external fields. Introducing a global order parameter, in
the replica-symmetric context, the problem is reduced to the analysis of the
solutions of a nonlinear integral equation. At zero temperature, and under some
restrictions on the form of the random fields, we are able to perform a
detailed analysis of stability of the replica-symmetric solutions. In contrast
to the behaviour of the Sherrington-Kirkpatrick model for a spin glass in a
uniform field, the paramagnetic solution is fully stable in a sufficiently
large random field
Diluted antiferromagnet in a ferromagnetic enviroment
The question of robustness of a network under random ``attacks'' is treated
in the framework of critical phenomena. The persistence of spontaneous
magnetization of a ferromagnetic system to the random inclusion of
antiferromagnetic interactions is investigated. After examing the static
properties of the quenched version (in respect to the random antiferromagnetic
interactions) of the model, the persistence of the magnetization is analysed
also in the annealed approximation, and the difference in the results are
discussed
Physical properties of the Schur complement of local covariance matrices
General properties of global covariance matrices representing bipartite
Gaussian states can be decomposed into properties of local covariance matrices
and their Schur complements. We demonstrate that given a bipartite Gaussian
state described by a covariance matrix \textbf{V}, the
Schur complement of a local covariance submatrix of it can be
interpreted as a new covariance matrix representing a Gaussian operator of
party 1 conditioned to local parity measurements on party 2. The connection
with a partial parity measurement over a bipartite quantum state and the
determination of the reduced Wigner function is given and an operational
process of parity measurement is developed. Generalization of this procedure to
a -partite Gaussian state is given and it is demonstrated that the
system state conditioned to a partial parity projection is given by a
covariance matrix such as its block elements are Schur complements
of special local matrices.Comment: 10 pages. Replaced with final published versio
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