The Critical 2d Ising Model On The Strip As A Boundary Conformal Field Theory

Résumé: In this work, we propose to identify the conformal field theory that describes the singularity of the 2D Ising model on an infinite strip with free boundary conditions. We will, first take the anisotropic limit where each critical point of the 2D Ising model with free boundary condition on the infinite strip will correspond to a critical point of the Ising spin chain with free boundary conditions at its end. Then, we use finite-size scaling behavior to measure the low-lying excitation spectrum of the quantum spin chain for the desired boundary condition. The measured spectrum is then compared with the spectra of the BCFTs candidate. The present dissertation is organized as follows. In chapter 1 we recall the basic concepts of statistical mechanics and critical phenomena. In the last section we will show how the finite-size scaling behavior and the phenomenological renormalization procedure can be performed to locate the critical points of statistical models. The second chapter is devoted to the general concepts and techniques of 2D conformal field theories. In particular for those defined on bounded geometries we study the consequences of the existence of boundaries on the conformal algebra and we determine the consistent boundary states as well as the partition functions of the CFTs one can define on such geometries. In the last chapter we measure the excitation spectrum of the quantum spin chain with free boundary conditions and compare it with the spectra of the BCFTs constructed from the (A31 A2) conformal theory.

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