Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum critical behavior of the quantum Ising model on fractal lattices   I study the properties of the quantum critical point of the transverse-field
quantum Ising model on various fractal lattices such as the Sierpi\'nski
carpet, Sierpi\'nski gasket, and Sierpi\'nski tetrahedron. Using a
continuous-time quantum Monte Carlo simulation method and the finite-size
scaling analysis, I identify the quantum critical point and investigate its
scaling properties. Among others, I calculate the dynamic critical exponent and
find that it is greater than one for all three structures. The fact that it
deviates from one is a direct consequence of the fractal structures not being
integer-dimensional regular lattices. Other critical exponents are also
calculated. The exponents are different from those of the classical critical
point, and satisfy the quantum scaling relation, thus confirming that I have
indeed found the quantum critical point. I find that the Sierpi\'nski
tetrahedron, of which the dimension is exactly two, belongs to a different
universality class than that of the two-dimensional square lattice. I conclude
that the critical exponents depend on more details of the structure than just
the dimension and the symmetry.

9
The categories of this paper are: nlin
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
2
The categories of this paper are: math
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th