### Abstract

We consider the quantum mechanical Ising ferromagnet in a strong transverse magnetic field in nay number of dimensions, d. We prove that in the ground state the power law correction to the exponential decay of the two point function is d/2. The proof begins by writing the ground state as a classical system in one more dimension. (Thus the classical Ornstein-Zernike power of (d-1)/2 becomes d/2). We then develop a convergent polymer expansion and use the techniques of Bricmont and Fröhlich [5].

Original language | English (US) |
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Pages (from-to) | 599-615 |

Number of pages | 17 |

Journal | Communications in Mathematical Physics |

Volume | 137 |

Issue number | 3 |

DOIs | |

State | Published - Apr 1991 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

### Cite this

**Ornstein-Zernike decay in the ground state of the quantum Ising model in a strong transverse field.** / Kennedy, Thomas G.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Ornstein-Zernike decay in the ground state of the quantum Ising model in a strong transverse field

AU - Kennedy, Thomas G

PY - 1991/4

Y1 - 1991/4

N2 - We consider the quantum mechanical Ising ferromagnet in a strong transverse magnetic field in nay number of dimensions, d. We prove that in the ground state the power law correction to the exponential decay of the two point function is d/2. The proof begins by writing the ground state as a classical system in one more dimension. (Thus the classical Ornstein-Zernike power of (d-1)/2 becomes d/2). We then develop a convergent polymer expansion and use the techniques of Bricmont and Fröhlich [5].

AB - We consider the quantum mechanical Ising ferromagnet in a strong transverse magnetic field in nay number of dimensions, d. We prove that in the ground state the power law correction to the exponential decay of the two point function is d/2. The proof begins by writing the ground state as a classical system in one more dimension. (Thus the classical Ornstein-Zernike power of (d-1)/2 becomes d/2). We then develop a convergent polymer expansion and use the techniques of Bricmont and Fröhlich [5].

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U2 - 10.1007/BF02100280

DO - 10.1007/BF02100280

M3 - Article

VL - 137

SP - 599

EP - 615

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -