Abstract
The rounding of first-order phase transitions by quenched randomness is stated in a form which is applicable to both classical and quantum systems: The free energy, as well as the ground state energy, of a spin system on a d-dimensional lattice is continuously differentiable with respect to any parameter in the Hamiltonian to which some randomness has been added when d ≤ 2. This implies absence of jumps in the associated order parameter, e.g., the magnetization in the case of a random magnetic field. A similar result applies in cases of continuous symmetry breaking for d ≤ 4. Some questions concerning the behavior of related order parameters in such random systems are discussed.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 2902-2906 |
| Number of pages | 5 |
| Journal | Physica A: Statistical Mechanics and its Applications |
| Volume | 389 |
| Issue number | 15 |
| DOIs | |
| State | Published - Aug 1 2010 |
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Condensed Matter Physics
Keywords
- Lattice spin systems
- Quenched disorder
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Greenblatt, R. L., Aizenman, M., & Lebowitz, J. L. (2010). On spin systems with quenched randomness: Classical and quantum. Physica A: Statistical Mechanics and its Applications, 389(15), 2902-2906. https://doi.org/10.1016/j.physa.2009.12.066