Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Criticality and quenched disorder: rare regions vs. Harris criterion   We employ scaling arguments and optimal fluctuation theory to establish a
general relation between quantum Griffiths singularities and the Harris
criterion for quantum phase transitions in disordered systems. If a clean
critical point violates the Harris criterion, it is destabilized by weak
disorder. At the same time, the Griffiths dynamical exponent $z'$ diverges upon
approaching the transition, suggesting unconventional critical behavior. In
contrast, if the Harris criterion is fulfilled, power-law Griffiths
singularities can coexist with clean critical behavior but $z'$ saturates at a
finite value. We present applications of our theory to a variety of systems
including quantum spin chains, classical reaction-diffusion systems and
metallic magnets; and we discuss modifications for transitions above the upper
critical dimension. Based on these results we propose a unified classification
of phase transitions in disordered systems.

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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: cs
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom