On Spin Systems with Quenched Randomness: Classical and Quantum

Details On Spin Systems with Quenched Randomness: Classical and Quantum On Spin Systems with Quenched Randomness: Classical and Quantum

2009-12-07

arxiv.org/abs/0912.1251v1

Physica A (2010) 389: 2902-2906

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

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 $d \leq 2$. 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 $d \leq 4$. Some questions concerning the behavior of related order parameters in such random systems are discussed.

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