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

TL;DR

This paper computes high-temperature series expansions for the bond-diluted Ising model in three to five dimensions, analyzing critical behavior and crossover effects due to quenched disorder using extrapolation methods.

Contribution

It provides new high-temperature series data and analysis for the diluted Ising model in higher dimensions, confirming theoretical predictions and identifying crossover phenomena.

Findings

Critical behavior in 4 and 5 dimensions governed by pure fixed point.

Logarithmic corrections in 4D Ising model confirmed.

Estimated critical exponent γ ≈ 1.305 in 3D at the random fixed point.

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.