Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Critical properties of Ising model on Sierpinski fractals. A finite size
  scaling analysis approach   The present paper focuses on the order-disorder transition of an Ising model
on a self-similar lattice. We present a detailed numerical study, based on the
Monte Carlo method in conjunction with the finite size scaling method, of the
critical properties of the Ising model on some two dimensional deterministic
fractal lattices with different Hausdorff dimensions. Those with finite
ramification order do not display ordered phases at any finite temperature,
whereas the lattices with infinite connectivity show genuine critical behavior.
In particular we considered two Sierpinski carpets constructed using different
generators and characterized by Hausdorff dimensions d_H=log 8/log 3 = 1.8927..
and d_H=log 12/log 4 = 1.7924.., respectively.
  The data show in a clear way the existence of an order-disorder transition at
finite temperature in both Sierpinski carpets.
  By performing several Monte Carlo simulations at different temperatures and
on lattices of increasing size in conjunction with a finite size scaling
analysis, we were able to determine numerically the critical exponents in each
case and to provide an estimate of their errors.
  Finally we considered the hyperscaling relation and found indications that it
holds, if one assumes that the relevant dimension in this case is the Hausdorff
dimension of the lattice.

16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
2
The categories of this paper are: math
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an