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Disorder-induced rounding of certain quantum phase transitions
1Department of Physics, University of Missouri-Rolla, Rolla, Missouri 65409, USA.
Physical Review Letters
|April 12, 2003
Summary
Quenched disorder rounds sharp quantum phase transitions in systems with overdamped dynamics. Rare spatial regions enable static order, leading to exponential dependence, while finite temperatures restore transitions with double-exponential scaling.
Area of Science:
- Condensed Matter Physics
- Quantum Phase Transitions
Background:
- Quantum phase transitions (QPTs) are fundamental to understanding many-body systems.
- Disorder effects are crucial for realistic physical systems, often altering critical behavior.
- Overdamped dynamics introduce unique complexities compared to Hamiltonian systems.
Purpose of the Study:
- Investigate the impact of quenched disorder on QPTs in systems with overdamped dynamics.
- Analyze how disorder influences the nature and characteristics of phase transitions.
- Determine the scaling relationships between order parameters, coupling constants, and temperature.
Main Methods:
- Theoretical analysis using Lifshitz-tail arguments.
- Numerical simulations of a model system exhibiting overdamped dynamics.
- Focus on systems with Ising order-parameter symmetry.
Main Results:
- Quenched disorder rounds sharp phase transitions by creating static order in rare spatial regions.
- This leads to an exponential dependence of the order parameter on the coupling constant.
- At finite temperatures, rare-region order is destroyed, restoring the phase transition with a double-exponential relationship between critical temperature and coupling strength.
Conclusions:
- Disorder fundamentally alters QPTs in overdamped systems, moving away from sharp transitions.
- The interplay between rare regions and finite temperature dictates the resulting scaling behavior.
- Lifshitz-tail arguments and simulations provide a consistent framework for understanding these effects.
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