Ising Model on Twisted Lattice and Holographic RG flow

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.