Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spin glass transitions of smectic-$A$ crosslinked elastomers   Elastomers are artificial polymeric materials created for industrial and
commercial applications. Depending on their purpose, they are performing in
different species and structure modifications. Our studies focus on the systems
of elastomers randomly standing-distributed in a smectic $A$ (Sm$A$) liquid
crystal. Basing on the suggestion following from the experiment, that at a
phase transition from Sm$A$ to nematic phase caused by an increase of a
crosslink concentration, such a system survives a percolation transition at low
crossilink concentrations, we propose a modeling explaining this phenomena. We
approve the three-dimensional Villain spin glass model and apply lattice Monte
Carlo (MC) techniques on differential forms on a dual lattice, that is an
alternative of a replica trick, developed for nematic elastomers in the 3D XY
universality. In the results of that we have confirmed a concentration phase
transition of percolation nature at a small crosslink concentration ($\sim$ 10
weight %).

27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci