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, hightemperature series expansions of the susceptibility 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 susceptibility to be γ = 1.305 (5)

High-temperature expansions of the higher susceptibilities for the Ising model in general dimensiond

“…HT This work 0.113920(1) * 0.092298(1) * 0.0777094(2) 0.067155(1) 0.059148(1) 0.052858(1) HT [37,41] 0.113935 (15) 0.092295(3) 0.077706(2) HT [42] 0.113915(3) MC [21] 0.113925 (12) 0.092290(5) 0.077706(2) 0.067144(4) MC [12,13] 0.11391(?) 0.09229(4) MC [14][15][16] 0.09229(4) 0.0777(1) 0.06712(4) MC [10] 0.1139152(4) MC [11] 0.1139139 (5) of the sequence (K (r) c ).…”

“…In d = 5 dimensions, our estimate is slightly larger than other estimates [10,11] of similar nominal accuracy, but can be essentially considered compatible with those of Refs. [21,37,41,42]. It is of interest to quote here also the estimate K c (5) = 0.113919(2) obtained from second-order quasidiagonal DAs that use all series coefficients up to order 20 l 22.…”

Site-diluted Ising model in four dimensions

“…The presence of the special exponential corrections has recently been verified by Hellmund and Janke in the case of the susceptibility [11]. These exponential terms mask the purely logarithmic corrections, so in order to detect and measure the latter one needs to cancel the former.…”

“…The consensus in the literature is that the following structure characterises the scaling behaviour of the specific heat, the susceptibility and the correlation length at the secondorder phase transition in the RSIM in four dimensions (up to higher-order correction to scaling terms) [6,7,8,9,10,11]:…”

Triviality problem and high-temperature expansions of higher susceptibilities for the Ising and scalar-field models in four-, five-, and six-dimensional lattices

“…On the other hand, for these systems high-temperature (HT) expansions have been until now derived only for a small number of observables and are too short [36][37][38], or, perhaps, barely adequate [39][40][41][42][43], to extract reliable information in the critical region. We believe, however, that the HT series methods might bring further insight into this context, provided that, for a conveniently enlarged set of observables, the lengths of the expansions can be significantly extended.…”