Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ising model on trees and factors of IID   We study the ferromagnetic Ising model on the infinite $d$-regular tree under
the free boundary condition. This model is known to be a factor of IID in the
uniqueness regime, when the inverse temperature $\beta\ge 0$ satisfies $\tanh
\beta \le (d-1)^{-1}$. However, in the reconstruction regime ($\tanh \beta >
(d-1)^{-\frac{1}{2}}$), it is not a factor of IID. We construct a factor of IID
for the Ising model beyond the uniqueness regime via a strong solution to an
infinite dimensional stochastic differential equation which partially answers a
question of Lyons. The solution $\{X_t(v) \}$ of the SDE is distributed as
  \[
  X_t(v) = t\tau_v + B_t(v),
  \] where $\{\tau_v \}$ is an Ising sample and $\{B_t(v) \}$ are independent
Brownian motions indexed by the vertices in the tree. Our construction holds
whenever $\tanh \beta \le c(d-1)^{-\frac{1}{2}}$, where $c>0$ is an absolute
constant.

12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas