Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite Size Effects in the Anisotropic \lambda/4!(\phi^4_1 + \phi^4_2)_d
  Model   We consider the $\frac{\lambda}{4!}(\phi^{4}_{1}+\phi^{4}_{2})$ model on a
d-dimensional Euclidean space, where all but one of the coordinates are
unbounded. Translation invariance along the bounded coordinate, z, which lies
in the interval [0,L], is broken because of the boundary conditions (BC's)
chosen for the hyperplanes z=0 and z=L. Two different possibilities for these
BC's boundary conditions are considered: DD and NN, where D denotes Dirichlet
and N Newmann, respectively. The renormalization procedure up to one-loop order
is applied, obtaining two main results. The first is the fact that the
renormalization program requires the introduction of counterterms which are
surface interactions. The second one is that the tadpole graphs for DD and NN
have the same z dependent part in modulus but with opposite signs. We
investigate the relevance of this fact to the elimination of surface
divergences.

10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol