Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The absence of phase transition for the classical XY-model on Sierpinski
  pyramid with fractal dimension D=2   For the spin models with continuous symmetry on regular lattices and finite
range of interactions the lower critical dimension is d=2. In two dimensions
the classical XY-model displays Berezinskii-Kosterlitz-Thouless transition
associated with unbinding of topological defects (vortices and antivortices).
We perform a Monte Carlo study of the classical XY-model on Sierpinski pyramids
whose fractal dimension is D=log4/log2=2 and the average coordination number
per site is about 7. The specific heat does not depend on the system size which
indicates the absence of long range order. From the dependence of the helicity
modulus on the cluster size and on boundary conditions we draw a conclusion
that in the thermodynamic limit there is no Berezinskii-Kosterlitz-Thouless
transition at any finite temperature. This conclusion is also supported by our
results for linear magnetic susceptibility. The lack of finite temperature
phase transition is presumably caused by the finite order of ramification of
Sierpinski pyramid.

14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph