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Rounding of first order transitions in low-dimensional quantum systems with quenched disorder
Rafael L Greenblatt1, Michael Aizenman, Joel L Lebowitz
1Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854-8019, USA. rafaelgr@physics.rutgers.edu
Physical Review Letters
|April 7, 2010
Summary
Adding small random perturbations to quantum spin systems rounds first-order phase transitions in low dimensions (d ≤ 2) or for continuous symmetry breaking (d ≤ 4). This rigorously proves the quantum Imry-Ma phenomenon.
Area of Science:
- Quantum physics
- Statistical mechanics
- Condensed matter theory
Background:
- First-order phase transitions are sharp changes in material properties.
- The Imry-Ma phenomenon describes how disorder can destabilize ordered phases in classical systems.
- Rigorous mathematical proofs for quantum systems are often challenging.
Purpose of the Study:
- To investigate the effect of random perturbations on quantum phase transitions.
- To rigorously establish the existence of the Imry-Ma phenomenon in quantum spin systems.
- To determine the dimensional limits for this effect.
Main Methods:
- Mathematical analysis of quantum spin systems with random perturbations.
- Focus on the behavior of the conjugate order parameter.
- Analysis in different spatial dimensions (d).
Main Results:
- Arbitrarily small random perturbations round first-order phase transitions in quantum spin systems.
- This effect is proven for d ≤ 2 dimensions.
- The phenomenon also holds for continuous symmetry breaking in d ≤ 4 dimensions.
Conclusions:
- The Imry-Ma phenomenon rigorously exists for quantum systems.
- Random perturbations play a crucial role in stabilizing disordered phases in quantum systems.
- The dimensional dependence of this phenomenon is established.
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