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