Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Percolation phase transition by removal of $k^{2}$-mers from fully
  occupied lattices   Numerical simulations and finite-size scaling analysis have been carried out
to study the problem of inverse site percolation by the removal of $k \times k$
square tiles ($k^{2}$-mers) from square lattices. The process starts with an
initial configuration, where all lattice sites are occupied and, obviously, the
opposite sides of the lattice are connected by occupied sites. Then, the system
is diluted by removing $k^{2}$-mers of occupied sites from the lattice
following a random sequential adsorption mechanism. The process finishes when
the jamming state is reached and no more objects can be removed due to the
absence of occupied sites clusters of appropriate size and shape. The central
idea of this paper is based on finding the maximum concentration of occupied
sites, $p_{c,k}$, for which the connectivity disappears. This particular value
of the concentration is called \textit{inverse percolation threshold}, and
determines a well-defined geometrical phase transition in the system. The
results obtained for $p_{c,k}$ show that the inverse percolation threshold is a
decreasing function of $k$ in the range $1 \leq k \leq 4$. For $k \geq 5$, all
jammed configurations are percolating states, and consequently, there is no
non-percolating phase. In other words, the lattice remains connected even when
the highest allowed concentration of removed sites is reached. The jamming
exponent $\nu_j$ was measured, being $\nu_j = 1$ regardless of the size $k$
considered. In addition, the accurate determination of the critical exponents
$\nu$, $\beta$ and $\gamma$ reveals that the percolation phase transition
involved in the system, which occurs for $k$ varying between 1 and 4, has the
same universality class as the standard percolation problem.

33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
2
The categories of this paper are: math
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph