Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
976144 | Physica A: Statistical Mechanics and its Applications | 2010 | 5 Pages |
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 dâ¤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 dâ¤4. Some questions concerning the behavior of related order parameters in such random systems are discussed.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Rafael L. Greenblatt, Michael Aizenman, Joel L. Lebowitz,