Abstract
We show how to obtain the critical exponent of magnetization in the Lee–Yang edge singularity model coupled to two-dimensional quantum gravity.
Highlights
We show how to obtain the critical exponent of magnetization in the Lee-Yang edge singularity model coupled to two-dimensional quantum gravity
Two-dimensional quantum Liouville gravity and the theory of random triangulations most likely describe the same theory, two-dimensional quantum gravity coupled to conformal field theories with a central charge c ≤ 1
The major problem of such a comparison has been to identify the observables to be compared in the two formulations
Summary
Two-dimensional quantum Liouville gravity and the theory of random triangulations (or matrix models) most likely describe the same theory, two-dimensional quantum gravity coupled to conformal field theories with a central charge c ≤ 1. The major problem of such a comparison has been to identify the observables to be compared in the two formulations. We will address an observable, the so-called “magnetization” at the Lee-Yang edge singularity. We will show how the general assumptions of operator mixing put forward in [1, 2, 3] allow us to obtain agreement between the critical exponent of the Lee-Yang “magnetization” calculated in quantum Liouville gravity and using matrix models. The rest of this article is organized as follows: we recapture how to calculate the magnetization exponent σ in the Ising model and at the LeeYang edge singularity using standard conformal field theory. In sec. 3 we show how to reconcile Liouville and matrix model results
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