Logarithmic Corrections for Spin Glasses, Percolation and Lee-Yang Singularities in Six Dimensions

TL;DR

This paper analytically derives logarithmic corrections to critical exponents and finite-size scaling in six-dimensional systems, including percolation, Lee-Yang singularities, and spin glasses, with validation against numerical simulations.

Contribution

It provides the first comprehensive analytical calculation of logarithmic corrections for various models at their upper critical dimension, including spin glasses and lattice animals.

Findings

Good agreement with numerical simulations for Ising spin glasses.

Derived formulas for logarithmic corrections in percolation and Lee-Yang singularities.

Extended results to compute corrections for lattice animals in eight dimensions.

Abstract

We study analytically the logarithmic corrections to the critical exponents of the critical behavior of correlation length, susceptibility and specific heat for the temperature and the finite-size scaling behavior, for a generic $\phi^3$ 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 formulas to the following special cases: percolation, Lee-Yang (LY) 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.