Influence of rare regions on the critical properties of systems with quenched disorder

We study the quantum phase transition of an itinerant antiferromagnet with cubic anisotropy in the presence of quenched disorder, paying particular attention to the locally ordered spatial regions that form in the Griffiths region. We derive an effective action where these rare regions are described in terms of static annealed disorder. A one-loop renormalization-group analysis of the effective action shows that for order-parameter dimensions $p<4,$ the rare regions destroy the conventional critical behavior, and the renormalized disorder flows to infinity. For order-parameter dimensions $p>4,$ the critical behavior is not influenced by the rare regions; it is described by the conventional dirty cubic fixed point. We also discuss the influence of the rare regions on the fluctuation-driven first-order transition in this system.We study the quantum phase transition of an itinerant antiferromagnet with cubic anisotropy in the presence of quenched disorder, paying particular attention to the locally ordered spatial regions that form in the Griffiths region. We derive an effective action where these rare regions are described in terms of static annealed disorder. A one-loop renormalization-group analysis of the effective action shows that for order-parameter dimensions $p<4,$ the rare regions destroy the conventional critical behavior, and the renormalized disorder flows to infinity. For order-parameter dimensions $p>4,$ the critical behavior is not influenced by the rare regions; it is described by the conventional dirty cubic fixed point. We also discuss the influence of the rare regions on the fluctuation-driven first-order transition in this system.

arXiv:cond-mat/0004013Physical review. B, Condensed matterDec 11, 20002 citations

Critical behavior of spin systems with quenched disorder

Akai Kurbanovich Murtazaev, Ibragimkhan K. Kamilov, Albert Babaevich Babaev

Journal of Magnetism and Magnetic MaterialsNov 19, 20054 citations

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

Thomas Vojta, Rastko Sknepnek

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.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.

Jan 1, 200417 citations

p<4,

the rare regions destroy the conventional critical behavior, and the renormalized disorder flows to infinity. For order-parameter dimensions

p>4,

the critical behavior is not influenced by the rare regions; it is described by the conventional dirty cubic fixed point. We also discuss the influence of the rare regions on the fluctuation-driven first-order transition in this system.