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Linking numbers for self-avoiding loops and percolation: application to the spin quantum hall transition
1Department of Physics-Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, United Kingdom and All Souls College, Oxford, United Kingdom.
Physical Review Letters
|October 6, 2000
Summary
New nonlocal twist operators precisely quantify self-avoiding loops and percolation clusters in 2D models. This allows exact calculation of critical properties, including conductivity at the spin Hall transition.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
- Quantum Field Theory
Background:
- Understanding critical phenomena in 2D models like O(n) and Q-state Potts is crucial.
- Nonlocal operators offer a powerful tool for analyzing complex systems.
Purpose of the Study:
- Introduce nonlocal twist operators for O(n) and Q-state Potts models.
- Exactly compute scaling dimensions and critical properties.
Main Methods:
- Development and application of nonlocal twist operators.
- Exact calculation of scaling dimensions for loops and clusters.
- Analysis of critical behavior near phase transitions.
Main Results:
- Exact computation of scaling dimensions for nonlocal twist operators.
- Quantification of percolation clusters needed to bridge distances.
- Determination of conductivity at the spin Hall transition as $\sqrt[3]{3}/2$.
- Analysis of shape-dependent mean conductance.
Conclusions:
- Nonlocal twist operators provide exact insights into critical phenomena.
- The study offers precise values for key physical quantities in 2D models.
- Applications extend to conductivity and conductance in specific geometries.