Ising Model on Twisted Lattice and Holographic RG flow

Abstract

The partition function of the two-dimensional Ising model is exactly obtained on a lattice with a twisted boundary condition. The continuum limit of the model off the critical temperature is found to give the mass-deformed Ising conformal field theory (CFT) on the torus with the complex structure $\tau$. We find that the renormalization group (RG) flow of the mass parameter can be holographically described in terms of the three-dimensional gravity including a scalar field with a simple nonlinear kinetic function and a quadratic potential.

27 pages, 3 figures, references added, comments added, typos corrected, a phase factor is added to the definition of the shift matrix, derivation of the partition function is refined

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