Free Variable Loop Equations for the 3-State Potts Model Coupled to 2D Gravity - INSPIRE

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Free Variable Loop Equations for the 3-State Potts Model Coupled to 2D Gravity

Aravinth Kulanthaivelu
(
- Oxford U., Theor. Phys.
)

Oct 31, 2019

17 pages

e-Print:

1911.00032 [math-ph]

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Abstract: (arXiv)

We revisit the long standing problem of the geometric free variable approach to computing the generating function for disk amplitudes in the matrix model formulation of the 3-state Potts model coupled to 2D discrete gravity. This method is a mild generalisation of Schwinger Dyson (loop-)equations approach, using graphical arguments to derive a single generating equation in non-commutative variables that contain the information of all loop equations. The method of constructing the generating equation is reviewed, we explain how a larger class of constraints than previously known can be constructed and we derive a closed set of equations that determine the spectral curve for the planar graph generating function.

Note:

17 pages

gravitation: discrete
loop equation
Potts model
noncommutative
matrix model
dimension: 2

References(21)

Figures(0)

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