1,573 research outputs found
A topological spin glass in diluted spin ice
It is a salient experimental fact that a large fraction of candidate spin
liquid materials freeze as the temperature is lowered. The question naturally
arises whether such freezing is intrinsic to the spin liquid ("disorder-free
glassiness") or extrinsic, in the sense that a topological phase simply
coexists with standard freezing of impurities. Here, we demonstrate a
surprising third alternative, namely that freezing and topological liquidity
are inseparably linked. The topological phase reacts to the introduction of
disorder by generating degrees of freedom of a new type (along with
interactions between them), which in turn undergo a freezing transition while
the topological phase supporting them remains intact.Comment: 4 pages + supplementary materia
Extinction window of mean field branching annihilating random walk
We study a model of growing population that competes for resources. At each
time step, all existing particles reproduce and the offspring randomly move to
neighboring sites. Then at any site with more than one offspring, the particles
are annihilated. This is a nonmonotone model, which makes the analysis more
difficult. We consider the extinction window of this model in the finite
mean-field case, where there are sites but movement is allowed to any site
(the complete graph). We show that although the system survives for exponential
time, the extinction window is logarithmic.Comment: Published at http://dx.doi.org/10.1214/14-AAP1069 in the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
On reverse hypercontractivity
We study the notion of reverse hypercontractivity. We show that reverse
hypercontractive inequalities are implied by standard hypercontractive
inequalities as well as by the modified log-Sobolev inequality. Our proof is
based on a new comparison lemma for Dirichlet forms and an extension of the
Strook-Varapolos inequality.
A consequence of our analysis is that {\em all} simple operators L=Id-\E as
well as their tensors satisfy uniform reverse hypercontractive inequalities.
That is, for all and every positive valued function for we have . This should
be contrasted with the case of hypercontractive inequalities for simple
operators where is known to depend not only on and but also on the
underlying space.
The new reverse hypercontractive inequalities established here imply new
mixing and isoperimetric results for short random walks in product spaces, for
certain card-shufflings, for Glauber dynamics in high-temperatures spin systems
as well as for queueing processes. The inequalities further imply a
quantitative Arrow impossibility theorem for general product distributions and
inverse polynomial bounds in the number of players for the non-interactive
correlation distillation problem with -sided dice.Comment: Final revision. Incorporates referee's comments. The proof of
appendix B has been corrected. A shorter version of this article will appear
in GAF
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