Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quasi-polynomial mixing of the 2D stochastic Ising model with "plus"
  boundary up to criticality   We considerably improve upon the recent result of Martinelli and Toninelli on
the mixing time of Glauber dynamics for the 2D Ising model in a box of side $L$
at low temperature and with random boundary conditions whose distribution $P$
stochastically dominates the extremal plus phase. An important special case is
when $P$ is concentrated on the homogeneous all-plus configuration, where the
mixing time $T_{mix}$ is conjectured to be polynomial in $L$. In [MT] it was
shown that for a large enough inverse-temperature $\beta$ and any $\epsilon >0$
there exists $c=c(\beta,\epsilon)$ such that $\lim_{L\to\infty}P(T_{mix}\geq
\exp({c L^\epsilon}))=0$. In particular, for the all-plus boundary conditions
and $\beta$ large enough $T_{mix} \leq \exp({c L^\epsilon})$.
  Here we show that the same conclusions hold for all $\beta$ larger than the
critical value $\beta_c$ and with $\exp({c L^\epsilon})$ replaced by $L^{c \log
L}$ (i.e. quasi-polynomial mixing). The key point is a modification of the
inductive scheme of [MT] together with refined equilibrium estimates that hold
up to criticality, obtained via duality and random-line representation tools
for the Ising model. In particular, we establish new precise bounds on the law
of Peierls contours which quantitatively sharpen the Brownian bridge picture
established e.g. in [Greenberg-Ioffe (2005)],[Higuchi (1979)],[Hryniv (1998)].

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The categories of this paper are: hep-lat
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th