Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite size behaviors of critical Ising model on a rectangle with free
  boundaries   Using the bond-propagation algorithm, we study the Ising model on a rectangle
of size $M \times N$ with free boundaries. For five aspect ratios
$\rho=M/N=1,2,4,8,16$, the critical free energy, internal energy and specific
heat are calculated. The largest size reached is $M \times N=64\times 10^6$.
The accuracy of the free energy reaches $10^{-26}$. Basing on these accurate
data, we determine exact expansions of the critical free energy, internal
energy and specific heat. With these expansions, we extract the bulk, surface
and corner parts of free energy, internal energy and specific heat. The fitted
bulk free energy density is given by $f_{\infty}=0.92969539834161021499(1)$,
comparing with Onsager's exact result $f_{\infty}=0.92969539834161021506...$.
We prove the conformal field theory(CFT) prediction of the corner free energy,
in which the central charge of the Ising model is found to be $c=0.5\pm 1\times
10^{-10}$ comparing with the CFT result $c=0.5$. We find that not only the
corner free energy but also the corner internal energy and specific heat are
geometry independent, i.e., independent of aspect ratio. The implication of
this finding on the finite scaling is discussed. In the second order correction
of the free energy, we prove the geometry dependence predicted by CFT and find
out a geometry independent constant beyond CFT. High order corrections are also
obtained.

26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex