Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the mixing time of the 2D stochastic Ising model with "plus" boundary
  conditions at low temperature   We consider the Glauber dynamics for the 2D Ising model in a box of side L,
at inverse temperature $\beta$ and random boundary conditions $\tau$ whose
distribution P either stochastically dominates the extremal plus phase (hence
the quotation marks in the title) or is stochastically dominated by the
extremal minus phase. A particular case is when P is concentrated on the
homogeneous configuration identically equal to + (equal to -). For $\beta$
large enough we show that for any $\epsilon$ there exists $c=c(\beta,\epsilon)$
such that the corresponding mixing time $T_{mix}$ satisfies
$\lim_{L\to\infty}P(T_{mix}> \exp({cL^\epsilon})) =0$. In the non-random case
$\tau\equiv +$ (or $\tau\equiv -$), this implies that $T_{mix}<
\exp({cL^\epsilon})$. The same bound holds when the boundary conditions are all
+ on three sides and all - on the remaining one. The result, although still
very far from the expected Lifshitz behaviour $T_{mix}=O(L^2)$, considerably
improves upon the previous known estimates of the form $T_{mix}\le \exp({c
L^{1/2 + \epsilon}})$. The techniques are based on induction over length
scales, combined with a judicious use of the so-called "censoring inequality"
of Y. Peres and P. Winkler, which in a sense allows us to guide the dynamics to
its equilibrium measure.

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The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
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The categories of this paper are: eess