Logarithmic Corrections for Spin Glasses, Percolation and Lee-Yang Singularities in Six 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 ${\varphi }^3$ 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.

18 pages. We have extended the computation to lattice animals in eight dimensions. To be published in Journal of Physics A

References in corpus (3)

• Simplicity of State and Overlap Structure in Finite-Volume Realistic Spin Glasses
• The four dimensional site-diluted Ising model: a finite-size scaling study
• Measures of critical exponents in the four dimensional site percolation

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• Revisiting the Lee-Yang singularities in the four-dimensional Ising model: a tribute to the memory of Ralph Kenna
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• The torus plateau for the high-dimensional Ising model
• Non-Commutative weak measurements: Entanglement, Symmetry Breaking, and the Role of Readout
• Evidence of de Almeida-Thouless line below six dimensions