Exact solution of the O(n) model on a random lattice

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Standard

Exact solution of the O(n) model on a random lattice. / Eynard, B.; Kristjansen, C.

I: Nuclear Physics B, Bind 455, Nr. 3, 27.09.1995, s. 577-618.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Eynard, B & Kristjansen, C 1995, 'Exact solution of the O(n) model on a random lattice', Nuclear Physics B, bind 455, nr. 3, s. 577-618. https://doi.org/10.1016/0550-3213(95)00469-9

APA

Eynard, B., & Kristjansen, C. (1995). Exact solution of the O(n) model on a random lattice. Nuclear Physics B, 455(3), 577-618. https://doi.org/10.1016/0550-3213(95)00469-9

Vancouver

Eynard B, Kristjansen C. Exact solution of the O(n) model on a random lattice. Nuclear Physics B. 1995 sep. 27;455(3):577-618. https://doi.org/10.1016/0550-3213(95)00469-9

Author

Eynard, B. ; Kristjansen, C. / Exact solution of the O(n) model on a random lattice. I: Nuclear Physics B. 1995 ; Bind 455, Nr. 3. s. 577-618.

Bibtex

@article{5459ea4a5d7c4933aee1f85f28313092,
title = "Exact solution of the O(n) model on a random lattice",
abstract = "We present an exact solution of the O(n) model on a random lattice. The coupling constant space of our model is parametrized in terms of a set of moment variables and the same type of universality with respect to the potential as observed for the one-matrix model is found. In addition we find a large degree of universality with respect to n; namely for n gE ] - 2,2[ the solution can be presented in a form which is valid not only for any potential, but also for any n (not necessarily rational). The cases n = ±2 are treated separately. We give explicit expressions for the genus-zero contribution to the one- and two-loop correlators as well as for the genus-one contribution to the one-loop correlator and the free energy. It is shown how one can obtain from these results any multi-loop correlator and the free energy to any genus and the structure of the higher-genera contributions is described. Furthermore we describe how the calculation of the higher-genera contributions can be pursued in the scaling limit.",
author = "B. Eynard and C. Kristjansen",
year = "1995",
month = sep,
day = "27",
doi = "10.1016/0550-3213(95)00469-9",
language = "English",
volume = "455",
pages = "577--618",
journal = "Nuclear Physics, Section B",
issn = "0550-3213",
publisher = "Elsevier BV * North-Holland",
number = "3",

}

RIS

TY - JOUR

T1 - Exact solution of the O(n) model on a random lattice

AU - Eynard, B.

AU - Kristjansen, C.

PY - 1995/9/27

Y1 - 1995/9/27

N2 - We present an exact solution of the O(n) model on a random lattice. The coupling constant space of our model is parametrized in terms of a set of moment variables and the same type of universality with respect to the potential as observed for the one-matrix model is found. In addition we find a large degree of universality with respect to n; namely for n gE ] - 2,2[ the solution can be presented in a form which is valid not only for any potential, but also for any n (not necessarily rational). The cases n = ±2 are treated separately. We give explicit expressions for the genus-zero contribution to the one- and two-loop correlators as well as for the genus-one contribution to the one-loop correlator and the free energy. It is shown how one can obtain from these results any multi-loop correlator and the free energy to any genus and the structure of the higher-genera contributions is described. Furthermore we describe how the calculation of the higher-genera contributions can be pursued in the scaling limit.

AB - We present an exact solution of the O(n) model on a random lattice. The coupling constant space of our model is parametrized in terms of a set of moment variables and the same type of universality with respect to the potential as observed for the one-matrix model is found. In addition we find a large degree of universality with respect to n; namely for n gE ] - 2,2[ the solution can be presented in a form which is valid not only for any potential, but also for any n (not necessarily rational). The cases n = ±2 are treated separately. We give explicit expressions for the genus-zero contribution to the one- and two-loop correlators as well as for the genus-one contribution to the one-loop correlator and the free energy. It is shown how one can obtain from these results any multi-loop correlator and the free energy to any genus and the structure of the higher-genera contributions is described. Furthermore we describe how the calculation of the higher-genera contributions can be pursued in the scaling limit.

U2 - 10.1016/0550-3213(95)00469-9

DO - 10.1016/0550-3213(95)00469-9

M3 - Journal article

AN - SCOPUS:0001133908

VL - 455

SP - 577

EP - 618

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

SN - 0550-3213

IS - 3

ER -

ID: 186918844