Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase transition of four-dimensional lattice $\phi^4$ theory with tensor
  renormalization group   We investigate the phase transition of the four-dimensional single-component
$\phi^4$ theory on the lattice using the tensor renormalization group method.
We have examined the hopping parameter dependence of the bond energy and the
vacuum condensation of the scalar field $\langle\phi\rangle$ at a finite
quartic coupling $\lambda$ on large volumes up to $V=1024^4$ in order to detect
the spontaneous breaking of the $\mathbb{Z}_2$ symmetry. Our results show that
the system undergoes the weak first-order phase transition at a certain
critical value of the hopping parameter. We also make a comparative study of
the three-dimensional $\phi^4$ theory and find that the properties of the phase
transition are consistent with the universality class of the three-dimensional
Ising model.

13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
2
The categories of this paper are: math
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph