### Abstract

Supersymmetric quantum mechanics is well known to provide, together with the so-called shape-invariance condition, an elegant method of solving the eigenvalue problem of some one-dimensional potentials by simple algebraic manipulations. In the present paper, this method is used in statistical physics. We consider the local critical behaviour of inhomogeneous Ising models and determine the complete set of anomalous dimensions from the spectrum of the corresponding transfer matrix in the strip geometry. For smoothly varying perturbations, the eigenvalue problem of the transfer matrix takes the form of a Schrodinger equation, and, furthermore, the corresponding potential exhibits the shape-invariance property for some known extended defects. In these cases, the complete spectrum is derived by the methods of supersymmetric quantum mechanics.

Original language | English |
---|---|

Article number | 005 |

Pages (from-to) | 3579-3590 |

Number of pages | 12 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 28 |

Issue number | 13 |

DOIs | |

Publication status | Published - 1995 |

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### ASJC Scopus subject areas

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

### Cite this

*Journal of Physics A: Mathematical and General*,

*28*(13), 3579-3590. [005]. https://doi.org/10.1088/0305-4470/28/13/005

**Realization of supersymmetric quantum mechanics in inhomogeneous Ising models.** / Berche, B.; Iglói, F.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 28, no. 13, 005, pp. 3579-3590. https://doi.org/10.1088/0305-4470/28/13/005

}

TY - JOUR

T1 - Realization of supersymmetric quantum mechanics in inhomogeneous Ising models

AU - Berche, B.

AU - Iglói, F.

PY - 1995

Y1 - 1995

N2 - Supersymmetric quantum mechanics is well known to provide, together with the so-called shape-invariance condition, an elegant method of solving the eigenvalue problem of some one-dimensional potentials by simple algebraic manipulations. In the present paper, this method is used in statistical physics. We consider the local critical behaviour of inhomogeneous Ising models and determine the complete set of anomalous dimensions from the spectrum of the corresponding transfer matrix in the strip geometry. For smoothly varying perturbations, the eigenvalue problem of the transfer matrix takes the form of a Schrodinger equation, and, furthermore, the corresponding potential exhibits the shape-invariance property for some known extended defects. In these cases, the complete spectrum is derived by the methods of supersymmetric quantum mechanics.

AB - Supersymmetric quantum mechanics is well known to provide, together with the so-called shape-invariance condition, an elegant method of solving the eigenvalue problem of some one-dimensional potentials by simple algebraic manipulations. In the present paper, this method is used in statistical physics. We consider the local critical behaviour of inhomogeneous Ising models and determine the complete set of anomalous dimensions from the spectrum of the corresponding transfer matrix in the strip geometry. For smoothly varying perturbations, the eigenvalue problem of the transfer matrix takes the form of a Schrodinger equation, and, furthermore, the corresponding potential exhibits the shape-invariance property for some known extended defects. In these cases, the complete spectrum is derived by the methods of supersymmetric quantum mechanics.

UR - http://www.scopus.com/inward/record.url?scp=33747061385&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33747061385&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/28/13/005

DO - 10.1088/0305-4470/28/13/005

M3 - Article

AN - SCOPUS:33747061385

VL - 28

SP - 3579

EP - 3590

JO - Journal Physics D: Applied Physics

JF - Journal Physics D: Applied Physics

SN - 0022-3727

IS - 13

M1 - 005

ER -