scholarly journals Benford analysis of quantum critical phenomena: First digit provides high finite-size scaling exponent while first two and further are not much better

2018 ◽  
Vol 382 (25) ◽  
pp. 1639-1644
Author(s):  
Anindita Bera ◽  
Utkarsh Mishra ◽  
Sudipto Singha Roy ◽  
Anindya Biswas ◽  
Aditi Sen(De) ◽  
...  
Keyword(s):  
Critical Phenomena ◽  
Finite Size ◽  
Scaling Exponent ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Quantum Critical Phenomena ◽  
Quantum Critical

Phase Transitions, Critical Phenomena, and Finite-Size Scaling

2019 ◽  
pp. 111-176
Author(s):  
Hans-Peter Eckle
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Critical Phenomena ◽  
Quantum Phase Transitions ◽  
Finite Size ◽  
System Size ◽  
Thermal Fluctuations ◽  
Finite Size Scaling ◽  
Size Scaling

Interacting many-particle systems may undergo phase transitions and exhibit critical phenomena in the limit of infinite system size, while the precursors of these phenomena are studied in the theory of finite-size scaling. After surveying the basic notions of phases, phase diagrams, and phase transitions, this chapter focuses on critical behaviour at a second-order phase transition. The Landau-Ginzburg theory and the concept of scaling prepare readers for an elementary introduction to the concepts of the renormalization group, followed by an introduction into the field of quantum phase transitions where quantum fluctuations take over the role of thermal fluctuations.

Finite-size scaling law in single-crystalline Fe3O4 hollow nanostructures

2016 ◽  
Vol 30 (21) ◽  
pp. 1650241 ◽  
Author(s):  
Xiaoping Zhang ◽  
Jun Wang ◽  
Miao Gao
Keyword(s):  
Scaling Law ◽  
Finite Size ◽  
Scaling Exponent ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Scaling Relation ◽  
Single Crystalline ◽  
Size Scaling ◽  
Hollow Nanostructures ◽  
Curie Temperatures

Single-crystalline Fe3O4 hollow nanostructures (nanoring and nanotube) have been successfully synthesized by a hydrothermal method along with a heat treatment process. The temperature dependences of the magnetization of the hollow nanostructures were measured under a high vacuum ([Formula: see text] Torr) from 300[Formula: see text]K to 900[Formula: see text]K. The Curie temperatures of the nanoring and nanotube samples were found to decrease with decreasing the mean wall thickness. The Curie temperatures of the hollow magnetite nanostructures follow a finite-size scaling relation with the scaling exponent [Formula: see text]. By comparison with those of the zero-dimensional Fe3O4 particles and two-dimensional Fe3O4 films, we show that the scaling relation for our hollow nanostructures is in better agreement with the quasi-two-dimensional finite-size scaling law.

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