High-temperature series for the bond-diluted Ising model in 3, 4 and 5 dimensions

Abstract

In order to study the influence of quenched disorder on second-order phase transitions, high-temperature series expansions of the \sus and the free energy are obtained for the quenched bond-diluted Ising model in $d=3$--5 dimensions. They are analysed using different extrapolation methods tailored to the expected singularity behaviours. In $d=4$ and 5 dimensions we confirm that the critical behaviour is governed by the pure fixed point up to dilutions near the geometric bond percolation threshold. The existence and form of logarithmic corrections for the pure Ising model in $d=4$ is confirmed and our results for the critical behaviour of the diluted system are in agreement with the type of singularity predicted by renormalization group considerations. In three dimensions we find large crossover effects between the pure Ising, percolation and random fixed point. We estimate the critical exponent of the \sus to be $\gamma =1.305(5)$ at the random fixed point.

arXiv comment16 pages, 10 figures

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• The high-temperature expansions of the higher susceptibilities for the Ising model in general dimension d
• Triviality problem and the high-temperature expansions of the higher susceptibilities for the Ising and the scalar field models on four-, five- and six-dimensional lattices
• Revising the universality class of the four-dimensional Ising model
• The Site-Diluted Ising Model in Four Dimension
• Exact solution and high temperature series expansion study of the 1/5-th depleted square lattice Ising model
• Localized magnetic moments in a Dirac semimetal as a spin model with long--range interactions