Critical points and quenched disorder: From Harris criterion to rare regions and smearing

Details Critical points and quenched disorder: From Harris criterion to rare regions and smearing Critical points and quenched disorder: From Harris criterion to rare regions and smearing

2004-05-04

arxiv.org/abs/cond-mat/0405070v2

phys. stat. sol. (b) 241, 2118 (2004)

Physics

Condensed Matter

Statistical Mechanics

10 pages, 5 eps figures, contribution to the Festschrift for Michael Schreiber's 50th birthday, final version as published

Scientific paper

10.1002/pssb.200404798

We consider the influence of quenched spatial disorder on phase transitions in classical and quantum systems. We show that rare strong disorder fluctuations can have dramatic effects on critical points. In classical systems with sufficiently correlated disorder or in quantum systems with overdamped dynamics they can completely destroy the sharp phase transition by smearing. This is caused by effects similar to but stronger than Griffiths phenomena: True static order can develop on a rare region while the bulk system is still in the disordered phase. We discuss the thermodynamic behavior in the vicinity of such a smeared transition using optimal fluctuation theory, and we present numerical results for a two-dimensional model system.

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