Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Free-energy distribution of the directed polymer at high temperature   We study the directed polymer of length $t$ in a random potential with fixed
endpoints in dimension 1+1 in the continuum and on the square lattice, by
analytical and numerical methods. The universal regime of high temperature $T$
is described, upon scaling 'time' $t \sim T^5/\kappa$ and space $x =
T^3/\kappa$ (with $\kappa=T$ for the discrete model) by a continuum model with
$\delta$-function disorder correlation. Using the Bethe Ansatz solution for the
attractive boson problem, we obtain all positive integer moments of the
partition function. The lowest cumulants of the free energy are predicted at
small time and found in agreement with numerics. We then obtain the exact
expression at any time for the generating function of the free energy
distribution, in terms of a Fredholm determinant. At large time we find that it
crosses over to the Tracy Widom distribution (TW) which describes the fixed $T$
infinite $t$ limit. The exact free energy distribution is obtained for any time
and compared with very recent results on growth and exclusion models.

3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
2
The categories of this paper are: math
12
The categories of this paper are: nucl-th