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

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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 languageEnglish (US)
Pages (from-to)599-615
Number of pages17
JournalCommunications in Mathematical Physics
Volume137
Issue number3
DOIs
StatePublished - Apr 1991

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Ising model
Ising Model
Ground State
Transverse
Decay
ground state
Ferromagnet
decay
Exponential Decay
Ising
Power Law
Polymers
Magnetic Field
expansion
polymers
magnetic fields

ASJC Scopus subject areas

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

Cite this

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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 Fr{\"o}hlich [5].",
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