Abstract

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 ω = (d−1)/(2d) in d dimensions. The stability of clean critical points is thus governed by the criterion (d+1)ν > 2 rather than the usual Harris criterion dν > 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.

Department(s)

Physics

Research Center/Lab(s)

Center for High Performance Computing Research

International Standard Serial Number (ISSN)

0031-9007

Document Type

Article - Journal

Document Version

Final Version

File Type

text

Language(s)

English

Rights

© 2014 American Physical Society (APS), All rights reserved.

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