Phase structure of the O(n) model on a random lattice for n > 2

B. Durhuus; C. Kristjansen

doi:10.1016/S0550-3213(96)00574-3

Phase structure of the O(n) model on a random lattice for n > 2

B. Durhuus^*, C. Kristjansen

^*Corresponding author for this work

12 Citations (Scopus)

Abstract

We show that coarse graining arguments invented for the analysis of multi-spin systems on a randomly triangulated surface apply also to the O(n) model on a random lattice. These arguments imply that if the model has a critical point with diverging string susceptibility, then either γ = +1/2 or there exists a dual critical point with negative string susceptibility exponent, γ̃, related to γ by γ = γ̃/γ̃-1. Exploiting the exact solution of the O(n) model on a random lattice we show that both situations are realized for n > 2 and that the possible dual pairs of string susceptibility exponents are given by (γ̃, γ) = (-1/m, 1/m+1), m = 2, 3, . . . We also show that at the critical points with positive string susceptibility exponent the average number of loops on the surface diverges while the average length of a single loop stays finite.

Original language	English
Journal	Nuclear Physics B
Volume	483
Issue number	3
Pages (from-to)	535-551
Number of pages	17
ISSN	0550-3213
DOIs	https://doi.org/10.1016/S0550-3213(96)00574-3
Publication status	Published - 13 Jan 1997

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title = "Phase structure of the O(n) model on a random lattice for n > 2",

abstract = "We show that coarse graining arguments invented for the analysis of multi-spin systems on a randomly triangulated surface apply also to the O(n) model on a random lattice. These arguments imply that if the model has a critical point with diverging string susceptibility, then either γ = +1/2 or there exists a dual critical point with negative string susceptibility exponent, {\~γ}, related to γ by γ = {\~γ}/{\~γ}-1. Exploiting the exact solution of the O(n) model on a random lattice we show that both situations are realized for n > 2 and that the possible dual pairs of string susceptibility exponents are given by ({\~γ}, γ) = (-1/m, 1/m+1), m = 2, 3, . . . We also show that at the critical points with positive string susceptibility exponent the average number of loops on the surface diverges while the average length of a single loop stays finite.",

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T1 - Phase structure of the O(n) model on a random lattice for n > 2

AU - Durhuus, B.

AU - Kristjansen, C.

PY - 1997/1/13

Y1 - 1997/1/13

N2 - We show that coarse graining arguments invented for the analysis of multi-spin systems on a randomly triangulated surface apply also to the O(n) model on a random lattice. These arguments imply that if the model has a critical point with diverging string susceptibility, then either γ = +1/2 or there exists a dual critical point with negative string susceptibility exponent, γ̃, related to γ by γ = γ̃/γ̃-1. Exploiting the exact solution of the O(n) model on a random lattice we show that both situations are realized for n > 2 and that the possible dual pairs of string susceptibility exponents are given by (γ̃, γ) = (-1/m, 1/m+1), m = 2, 3, . . . We also show that at the critical points with positive string susceptibility exponent the average number of loops on the surface diverges while the average length of a single loop stays finite.

AB - We show that coarse graining arguments invented for the analysis of multi-spin systems on a randomly triangulated surface apply also to the O(n) model on a random lattice. These arguments imply that if the model has a critical point with diverging string susceptibility, then either γ = +1/2 or there exists a dual critical point with negative string susceptibility exponent, γ̃, related to γ by γ = γ̃/γ̃-1. Exploiting the exact solution of the O(n) model on a random lattice we show that both situations are realized for n > 2 and that the possible dual pairs of string susceptibility exponents are given by (γ̃, γ) = (-1/m, 1/m+1), m = 2, 3, . . . We also show that at the critical points with positive string susceptibility exponent the average number of loops on the surface diverges while the average length of a single loop stays finite.

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U2 - 10.1016/S0550-3213(96)00574-3

DO - 10.1016/S0550-3213(96)00574-3

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SP - 535

EP - 551

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

IS - 3

ER -

Phase structure of the O(n) model on a random lattice for n > 2

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