Finite size scaling and universality in the (2+1)D Ising model

Abstract

The energy and magnetisation density of the (2+1)D Ising model are investigated. For the thermal exponent the author finds xepsilon =1.42+or-0.02, in agreement with hyperscaling. The Privman-Fisher universality hypothesis is confirmed by two methods. First, the author presents, at the critical point, numerical data for the finite-size scaling amplitudes of the (singular) free energy, magnetisation, susceptibility and surface tension and checks them for universality. Second, using the explicitly computed eigenvectors of the Hamiltonian, it is shown that the ratios of matrix elements of the energy and magnetisation density are universal.