Brazilian Journal of Physics

, 41:201 | Cite as

Interplay of Quantum and Classical Fluctuations Near Quantum Critical Points

  • Mucio Amado ContinentinoEmail author
Condensed Matter


For a system near a quantum critical point (QCP), above its lower critical dimension d L , there is in general a critical line of second-order phase transitions that separates the broken symmetry phase at finite temperatures from the disordered phase. The phase transitions along this line are governed by thermal critical exponents that are different from those associated with the quantum critical point. We point out that, if the effective dimension of the QCP, d eff = d + z (d is the Euclidean dimension of the system and z the dynamic quantum critical exponent) is above its upper critical dimension \(d_{_{C}}\) there is an intermingle of classical (thermal) and quantum critical fluctuations near the QCP. This is due to the breakdown of the generalized scaling relation ψ = νz between the shift exponent ψ of the critical line and the crossover exponent νz, for \(d+z>d_{_{C}}\) by a dangerous irrelevant interaction. This phenomenon has clear experimental consequences, like the suppression of the amplitude of classical critical fluctuations near the line of finite temperature phase transitions as the critical temperature is reduced approaching the QCP.


Strongly correlated electron systems Critical point phenomena Quantum phase transitions Renormalization-group theory 



I would like to thank Armando Paduan-Filho for useful discussions. I would like also to express my gratitude for the referee for suggestions and advices concerning the historical aspects of the development of the theory of quantum phase transitions. Work partially supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico and Fundação de Amparo a Pesquisa do Estado do Rio de Janeiro.


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Copyright information

© Sociedade Brasileira de Física 2011

Authors and Affiliations

  1. 1.Centro Brasileiro de Pesquisas FísicasRio de JaneiroBrazil

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