Ising Model on Twisted Lattice and Holographic RG flow

TL;DR

This paper derives the exact partition function of the 2D Ising model on a twisted lattice, explores its continuum limit as a mass-deformed CFT, and describes its RG flow holographically via 3D gravity with scalar fields.

Contribution

It provides an exact lattice partition function with twisted boundary conditions and connects the RG flow of the model to a holographic gravity description.

Findings

Exact partition function on twisted lattice obtained

Continuum limit yields mass-deformed Ising CFT on torus

Holographic description of RG flow via 3D gravity with scalar field

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.