scholarly journals Fidelity approach to quantum phase transitions: finite-size scaling for the quantum Ising model in a transverse field

2008 ◽  
Vol 41 (49) ◽  
pp. 492002 ◽  
Author(s):  
Huan-Qiang Zhou ◽  
Jian-Hui Zhao ◽  
Bo Li
Keyword(s):  
Phase Transitions ◽  
Ising Model ◽  
Quantum Phase Transitions ◽  
Finite Size ◽  
Transverse Field ◽  
Quantum Phase ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Quantum Ising Model

scholarly journals PERCOLATION AND FINITE SIZE SCALING IN SEVEN DIMENSIONS

2004 ◽  
Vol 15 (09) ◽  
pp. 1321-1325
Author(s):  
LOTFI ZEKRI
Keyword(s):  
Phase Transitions ◽  
Ising Model ◽  
Numerical Investigation ◽  
Critical Exponents ◽  
Finite Size ◽  
Critical Dimension ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Hypercubic Lattice

Numerical investigation of critical exponents on a hypercubic lattice with Ld random sites with L up to 33 and d up to 7 showed that above the critical dimension the phase transitions in Ising model and percolation are not alike.

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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