8,039 research outputs found
Ground-state configuration space heterogeneity of random finite-connectivity spin glasses and random constraint satisfaction problems
We demonstrate through two case studies, one on the p-spin interaction model
and the other on the random K-satisfiability problem, that a heterogeneity
transition occurs to the ground-state configuration space of a random
finite-connectivity spin glass system at certain critical value of the
constraint density. At the transition point, exponentially many configuration
communities emerge from the ground-state configuration space, making the
entropy density s(q) of configuration-pairs a non-concave function of
configuration-pair overlap q. Each configuration community is a collection of
relatively similar configurations and it forms a stable thermodynamic phase in
the presence of a suitable external field. We calculate s(q) by the
replica-symmetric and the first-step replica-symmetry-broken cavity methods,
and show by simulations that the configuration space heterogeneity leads to
dynamical heterogeneity of particle diffusion processes because of the entropic
trapping effect of configuration communities. This work clarifies the fine
structure of the ground-state configuration space of random spin glass models,
it also sheds light on the glassy behavior of hard-sphere colloidal systems at
relatively high particle volume fraction.Comment: 26 pages, 9 figures, submitted to Journal of Statistical Mechanic
Anisotropic Energy Gaps of Iron-based Superconductivity from Intra-band Quasiparticle Interference in LiFeAs
If strong electron-electron interactions between neighboring Fe atoms mediate
the Cooper pairing in iron-pnictide superconductors, then specific and distinct
anisotropic superconducting energy gaps \Delta_i(k) should appear on the
different electronic bands i. Here we introduce intra-band Bogoliubov
quasiparticle scattering interference (QPI) techniques for determination of
\Delta_i(k) in such materials, focusing on LiFeAs. We identify the three
hole-like bands assigned previously as \gamma, \alpha_2 and \alpha_1, and we
determine the anisotropy, magnitude and relative orientations of their
\Delta_i(k). These measurements will advance quantitative theoretical analysis
of the mechanism of Cooper pairing in iron-based superconductivity
Wall-crossing, open BPS counting and matrix models
We consider wall-crossing phenomena associated to the counting of D2-branes
attached to D4-branes wrapping lagrangian cycles in Calabi-Yau manifolds, both
from M-theory and matrix model perspective. Firstly, from M-theory viewpoint,
we review that open BPS generating functions in various chambers are given by a
restriction of the modulus square of the open topological string partition
functions. Secondly, we show that these BPS generating functions can be
identified with integrands of matrix models, which naturally arise in the free
fermion formulation of corresponding crystal models. A parameter specifying a
choice of an open BPS chamber has a natural, geometric interpretation in the
crystal model. These results extend previously known relations between open
topological string amplitudes and matrix models to include chamber dependence.Comment: 25 pages, 8 figures, published versio
- …