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arXiv · 0912.1251

On Spin Systems with Quenched Randomness: Classical and Quantum

Rafael L Greenblatt·Michael Aizenman·Joel L. Lebowitz
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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 $d \leq 2$. 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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Rafael L Greenblatt, Michael Aizenman, Joel L. Lebowitz. 2009-12-07. On Spin Systems with Quenched Randomness: Classical and Quantum. https://doi.org/10.1016/j.physa.2009.12.066

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