Excitation spectrum and density matrix renormalization group iterations
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This thesis explores two aspects of the renormalization group (RG) in quantum field theory (QFT). In the first part we study the structure of RG flows in general Poincaré-invariant, unitary QFTs, and in particular the irreversibility properties and the rel ...
We perform Monte-Carlo simulations of the three-dimensional Ising model at the critical temperature and zero magnetic field. We simulate the system in a ball with free boundary conditions on the two dimensional spherical boundary. Our results for one and t ...
We rigorously prove the existence and the conformal invariance of scaling limits of the magnetization and multi-point spin correlations in the critical Ising model on arbitrary simply connected planar domains. This solves a number of conjectures coming fro ...
We introduce a minimal model describing the physics of classical two-dimensional (2D) frustrated Heisenberg systems, where spins order in a nonplanar way at T=0. This model, consisting of coupled trihedra (or Ising-RP3 model), encompasses Ising (chiral) de ...
We study the 2-dimensional Ising model at critical temperature on a smooth simply-connected graph Ω.We rigorously prove the conformal invariance of arbitrary spin-pattern probabilities centered at a point a and derive formulas to compute the probabilities ...
We study the critical Ising model on the square lattice in bounded simply connected domains with + and free boundary conditions. We relate the energy density of the model to a discrete fermionic spinor and compute its scaling limit by discrete complex anal ...
Most two-dimensional massless field theories carry represe ntations of the Virasoro algebra as consequences of their conformal symmetry. Recently, conformal symmetry has been rigorously established for scaling limit s of lattice models by means of discrete ...
We study the possible IR and UV asymptotics of 4D Lorentz invariant unitary quantum field theory. Our main tool is a generalization of the Komargodski-Schwimmer proof for the alpha-theorem. We use this to rule out a large class of renormalization group flo ...
We review recent results with D. Chelkak and K. Izyurov, where we rigorously prove existence and conformal invariance of scaling limits of magnetization and multi-point spin correlations in the critical Ising model on an arbitrary simply connected planar d ...
