Introduction to Conformal Invariance and Finite-Size Scaling

John Cardy

J.G. Brankov

I. G. Brankov

John Cardy

The universal relation between critical exponents and the amplitude of the correlation length divergence as a function of finite size at the critical point of two-dimensional systems is shown to be a consequence of conformal invariance. Both periodic and free boundary conditions are considered.

Francisco Castilho Alcaraz, V. Rittenberg

In a conformal invariant one-dimensional stochastic model, a certain non-local perturbation takes the system to a new massless phase of a special kind. The ground-state of the system is an adsorptive state. Part of the finite-size scaling spectrum of the evolution Hamiltonian stays unchanged but some levels go exponentially to zero for large lattice sizes becoming degenerate with the ground-state. As a consequence one observes the appearance of quasistationary states which have a relaxation time which grows exponentially with the size of the system. Several initial conditions have singled out a quasistationary state which has in the finite-size scaling limit the same properties as the stationary state of the conformal invariant model.