4,975 research outputs found
Numerical study of a short-range p-spin glass model in three dimensions
In this work we study numerically a short range p-spin glass model in three
dimensions. The behaviour of the model appears to be remarkably different from
mean field predictions. In fact it shares some features typical of models with
full replica-symmetry breaking (FRSB). Nevertheless, we believe that the
transition that we study is intrinsically different from the FRSB and basically
due to non-perturbative contributions. We study both the statics and the
dynamics of the system which seem to confirm our conjectures.Comment: 20 pages, 15 figure
Split transition in ferromagnetic superconductors
The split superconducting transition of up-spin and down-spin electrons on
the background of ferromagnetism is studied within the framework of a recent
model that describes the coexistence of ferromagnetism and superconductivity
induced by magnetic fluctuations. It is shown that one generically expects the
two transitions to be close to one another. This conclusion is discussed in
relation to experimental results on URhGe. It is also shown that the magnetic
Goldstone modes acquire an interesting structure in the superconducting phase,
which can be used as an experimental tool to probe the origin of the
superconductivity.Comment: REVTeX4, 15 pp, 7 eps fig
Quantum critical behavior in disordered itinerant ferromagnets: Logarithmic corrections to scaling
The quantum critical behavior of disordered itinerant ferromagnets is
determined exactly by solving a recently developed effective field theory. It
is shown that there are logarithmic corrections to a previous calculation of
the critical behavior, and that the exact critical behavior coincides with that
found earlier for a phase transition of undetermined nature in disordered
interacting electron systems. This confirms a previous suggestion that the
unspecified transition should be identified with the ferromagnetic transition.
The behavior of the conductivity, the tunneling density of states, and the
phase and quasiparticle relaxation rates across the ferromagnetic transition is
also calculated.Comment: 15pp., REVTeX, 8 eps figs, final version as publishe
Wave localization in binary isotopically disordered one-dimensional harmonic chains with impurities having arbitrary cross section and concentration
The localization length for isotopically disordered harmonic one-dimensional
chains is calculated for arbitrary impurity concentration and scattering cross
section. The localization length depends on the scattering cross section of a
single scatterer, which is calculated for a discrete chain having a wavelength
dependent pulse propagation speed. For binary isotopically disordered systems
composed of many scatterers, the localization length decreases with increasing
impurity concentration, reaching a mimimum before diverging toward infinity as
the impurity concentration approaches a value of one. The concentration
dependence of the localization length over the entire impurity concentration
range is approximated accurately by the sum of the behavior at each limiting
concentration. Simultaneous measurements of Lyapunov exponent statistics
indicate practical limits for the minimum system length and the number of
scatterers to achieve representative ensemble averages. Results are discussed
in the context of future investigations of the time-dependent behavior of
disordered anharmonic chains.Comment: 8 pages, 10 figures, submitted to PR
Critical behaviour of combinatorial search algorithms, and the unitary-propagation universality class
The probability P(alpha, N) that search algorithms for random Satisfiability
problems successfully find a solution is studied as a function of the ratio
alpha of constraints per variable and the number N of variables. P is shown to
be finite if alpha lies below an algorithm--dependent threshold alpha\_A, and
exponentially small in N above. The critical behaviour is universal for all
algorithms based on the widely-used unitary propagation rule: P[ (1 + epsilon)
alpha\_A, N] ~ exp[-N^(1/6) Phi(epsilon N^(1/3)) ]. Exponents are related to
the critical behaviour of random graphs, and the scaling function Phi is
exactly calculated through a mapping onto a diffusion-and-death problem.Comment: 7 pages; 3 figure
Quantum Optimization for Combinatorial Searches
I propose a "quantum annealing" heuristic for the problem of combinatorial
search among a frustrated set of states characterized by a cost function to be
minimized. The algorithm is probabilistic, with postselection of the
measurement result. A unique parameter playing the role of an effective
temperature governs the computational load and the overall quality of the
optimization. Any level of accuracy can be reached with a computational load
independent of the dimension {\it N} of the search set by choosing the
effective temperature correspondingly low. This is much better than classical
search heuristics, which typically involve computation times growing as powers
of log({\it N})Comment: Revised, published versio
Quantum Annealing in the Transverse Ising Model
We introduce quantum fluctuations into the simulated annealing process of
optimization problems, aiming at faster convergence to the optimal state.
Quantum fluctuations cause transitions between states and thus play the same
role as thermal fluctuations in the conventional approach. The idea is tested
by the transverse Ising model, in which the transverse field is a function of
time similar to the temperature in the conventional method. The goal is to find
the ground state of the diagonal part of the Hamiltonian with high accuracy as
quickly as possible. We have solved the time-dependent Schr\"odinger equation
numerically for small size systems with various exchange interactions.
Comparison with the results of the corresponding classical (thermal) method
reveals that the quantum annealing leads to the ground state with much larger
probability in almost all cases if we use the same annealing schedule.Comment: 15 pages, RevTeX, 8 figure
Microscopic Theory of Heterogeneity and Non-Exponential Relaxations in Supercooled Liquids
Recent experiments and computer simulations show that supercooled liquids
around the glass transition temperature are "dynamically heterogeneous" [1].
Such heterogeneity is expected from the random first order transition theory of
the glass transition. Using a microscopic approach based on this theory, we
derive a relation between the departure from Debye relaxation as characterized
by the value of a stretched exponential response function , and the fragility of the liquid. The
value is also predicted to depend on temperature and to vanish as the ideal
glass transition is approached at the Kauzmann temperature.Comment: 4 pages including 3 eps figure
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