Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase Transitions on Random Lattices: How Random is Topological
  Disorder?   We study the effects of topological (connectivity) disorder on phase
transitions. We identify a broad class of random lattices whose disorder
fluctuations decay much faster with increasing length scale than those of
generic random systems, yielding a wandering exponent of $\omega=(d-1)/(2d)$ in
$d$ dimensions. %instead of the generic value $\omega=1/2$. The stability of
clean critical points is thus governed by the criterion $(d+1)\nu > 2$ rather
than the usual Harris criterion $d\nu>2$, making topological disorder less
relevant than generic randomness. The Imry-Ma criterion is also modified,
allowing first-order transitions to survive in all dimensions $d>1$. These
results explain a host of puzzling violations of the original criteria for
equilibrium and nonequilibrium phase transitions on random lattices. We discuss
applications, and we illustrate our theory by computer simulations of random
Voronoi and other lattices.

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The categories of this paper are: comp-gas
2
The categories of this paper are: math
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom