On Spin Systems with Quenched Randomness: Classical and Quantum

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 $d\le 2$. This implies absence of jumps in the associated order parameter, e.g., the magnetization in case of a random magnetic field. A similar result applies in cases of continuous symmetry breaking for $d\le 4$. Some questions concerning the behavior of related order parameters in such random systems are discussed.

8 pages LaTeX, 2 PDF figures. Presented by JLL at the symposium "Trajectories and Friends" in honor of Nihat Berker, MIT, October 2009

References in corpus (4)

• Rounding of First Order Transitions in Low-Dimensional Quantum Systems with Quenched Disorder
• Rounding by disorder of first-order quantum phase transitions: emergence of quantum critical points
• Percolation Phenomena in Low and High Density Systems
• Uncovering the secrets of the 2d random-bond Blume-Capel model

Cited by in corpus (7)

• Universality from disorder in the random-bond Blume-Capel model
• The effect of quenched bond disorder on first-order phase transitions
• Activated scaling in disorder rounded first-order quantum phase transitions
• Uncovering the secrets of the 2d random-bond Blume-Capel model
• Crumpled-to-flat transition of quenched disordered membranes at two-loop order
• Effects of Quenched Randomness on Classical and Quantum Phase Transitions
• Suppression of discontinuous phase transitions by particle diffusion