Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Anomalous mean-field behavior of the fully connected Ising model   Although the fully connected Ising model does not have a length scale, we
show that its critical exponents can be found using finite size scaling with
the scaling variable equal to N, the number of spins. We find that at the
critical temperature of the infinite system the mean value and the most
probable value of the magnetization scale differently with N, and the
probability distribution of the magnetization is not a Gaussian, even for large
N. Similar results inconsistent with the usual understanding of mean-field
theory are found at the spinodal. We relate these results to the breakdown of
hyperscaling and show how hyperscaling can be restored by increasing N while
holding the Ginzburg parameter rather than the temperature fixed.

16
The categories of this paper are: stat
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
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn