Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Thermodynamic formalism and large deviation principle of multiplicative
  Ising models   The aim of this study is tree-fold. First, we investigate the thermodynamics
of the Ising models with respect to 2-multiple Hamiltonians. This extends the
previous results of [Chazotte and Redig, Electron. J. Probably., 2014] to
$\mathbb{N}^d$. Second, we establish the large deviation principle (LDP) of the
average $\frac{1}{N} S_N^G$, where $S_N^G$ is a 2-multiple sum along a
semigroup generated by k numbers which are k co-primes. This extends the
previous results [Ban et al. Indag. Math., 2021] to a board class of the
long-range interactions. Finally, the results described above are generalized
to the multidimensional lattice $\mathbb{N}^d, d\geq1$.

9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an