New Method to Study Critical Phenomena–Mean-Field Finite-Size Scaling Theory

1986 ◽  
Vol 55 (1) ◽  
pp. 1-4 ◽  
Author(s):  
Masuo Suzuki ◽  
Makoto Katori
Keyword(s):  
Critical Phenomena ◽  
Mean Field ◽  
Finite Size ◽  
Scaling Theory ◽  
New Method ◽  
Finite Size Scaling ◽  
Size Scaling

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.

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