Finite-size scaling functions and conformal invariance

Abstract

A method to calculate perturbative corrections to the spectrum of a one-dimensional quantum chain in the scaling variable z is developed from the conformal invariance at its fixed point. Then, from the knowledge of certain correlation functions, one can calculate the first coefficients of the scaling functions. The method is applied successfully to the Ising model, where the corrections are also known from the exact solution. The first coefficients of the magnetic scaling functions of the Ising model are also obtained.