Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hamiltonian equation of motion and depinning phase transition in
  two-dimensional magnets   Based on the Hamiltonian equation of motion of the $\phi^4$ theory with
quenched disorder, we investigate the depinning phase transition of the
domain-wall motion in two-dimensional magnets. With the short-time dynamic
approach, we numerically determine the transition field, and the static and
dynamic critical exponents. The results show that the fundamental Hamiltonian
equation of motion belongs to a universality class very different from those
effective equations of motion.

25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con