Scaling theory and logarithmic singularities

M. Broidioi, M Van Canneyt

Mostafa Ghasemi, Shahrokh Parvizi

We study the entanglement entropy of theories that are derived from relevant perturbation of given CFTs for regions with a singular boundary by using the AdS/CFT correspondence. In the smooth case, it is well known that a relevant deformation of the boundary theory by the relevant operator with scaling dimension $Δ=\frac{d+2}{2}$ generates a logarithmic universal term to the entanglement entropy. As the smooth case, when the boundary CFT deformed by a relevant operator, we find that the entanglement entropy of singular surface also contains a new logarithmic term which is due to relevant perturbation of the conformal field theory, and depends on the scaling dimension of relevant operator. We also find for extended singular surfaces, $c_{n}\times R^{m}$, as well as logarithmic term, the new universal double logarithmic terms may appear depending on the scaling dimension of relevant operator and spacetime dimensions. These new terms are due to relevant perturbation of the boundary theory.

Juan Jesus Ruiz-Lorenzo

We study analytically the logarithmic corrections to the critical exponents of the critical behaviour of correlation length, susceptibility and specific heat for the temperature and the finite-size scaling behaviour, for a generic theory at its upper critical dimension (six). We have also computed the leading correction to scaling as a function of the lattice size. We distinguish the obtained formulae to the following special cases: percolation, Lee-Yang singularities and m -component spin glasses. We have compared our results for the Ising spin glass case with numerical simulations finding a very good agreement. Finally, and using the results obtained for the Lee-Yang singularities in six dimensions, we have computed the logarithmic corrections to the singular part of the free energy for lattice animals in eight dimensions.

V. N. Plechko

E. Brézin

In four dimensions mean field theory is not valid since scaling is violated by powers of logarithms. Therefore the theory is not the ε = 0 limit of the 4 - ε dimensional theory. However ratios of critical amplitudes are in most cases correctly described by this limit. In some cases, it is nevertheless necessary to be cautious, and an example is provided of a ratio which does not coincide with its mean field value.

Malte Henkel