### 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) |
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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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## Cite this

*Physica A: Statistical Mechanics and its Applications*,

*389*(15), 2902-2906. https://doi.org/10.1016/j.physa.2009.12.066