Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A variational formula for the free energy of the partially directed
  polymer collapse   Long linear polymers in dilute solutions are known to undergo a collapse
transition from a random coil (expand itself) to a compact ball (fold itself
up) when the temperature is lowered, or the solvent quality deteriorates. A
natural model for this phenomenon is a 1+1 dimensional self-interacting and
partially directed self-avoiding walk. In this paper, we develop a new method
to study the partition function of this model, from which we derive a
variational formula for the free energy. This variational formula allows us to
prove the existence of the collapse transition and to identify the critical
temperature in a simple way. We also prove that the order of the collapse
transition is 3/2.

16
The categories of this paper are: stat
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex