Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Annealed scaling for a charged polymer in dimensions two and higher   This paper considers an undirected polymer chain on $\mathbb{Z}^d$, $d \geq
2$, with i.i.d.\ random charges attached to its constituent monomers. Each
self-intersection of the polymer chain contributes an energy to the interaction
Hamiltonian that is equal to the product of the charges of the two monomers
that meet. The joint probability distribution for the polymer chain and the
charges is given by the Gibbs distribution associated with the interaction
Hamiltonian. The object of interest is the \emph{annealed free energy} per
monomer in the limit as the length $n$ of the polymer chain tends to infinity.
We show that there is a critical curve in the parameter plane spanned by the
charge bias and the inverse temperature separating an \emph{extended phase}
from a \emph{collapsed phase}. We derive the scaling of the critical curve for
small and for large charge bias and the scaling of the annealed free energy for
small inverse temperature, which are both anomalous. We show that in a subset
of the collapsed phase the polymer chain is \emph{subdiffusive}, namely, on
scale $(n/\log n)^{1/(d+2)}$ it moves like a Brownian motion conditioned to
stay inside a ball with a deterministic radius and a randomly shifted center.
We expect this scaling to hold throughout the collapsed phase. We further
expect that in the extended phase the polymer chain scales like a weakly
self-avoiding walk. Proofs are based on a detailed analysis for simple random
walk of the downward large deviations of the self-intersection local time and
the upward large deviations of the range. Part of our scaling results are
rough, and we formulate conjectures under which they can be sharpened. The
existence of the free energy remains an open problem, which we are able to
settle in a subset of the collapsed phase for a subclass of charge
distributions.

13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio