Physics – Condensed Matter – Statistical Mechanics
Scientific paper
1998-04-28
J.Phys.A31:8773-8787,1998
Physics
Condensed Matter
Statistical Mechanics
18 pages. We have extended the computation to lattice animals in eight dimensions. To be published in Journal of Physics A
Scientific paper
10.1088/0305-4470/31/44/006
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.
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