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Very-high energy observations of blazars can be used to constrain thestrength of the intergalactic magnetic field. A simplifying assumption which isoften made is that of a magnetic field of constant strength composed byrandomly oriented and identical cells. In this paper, we demonstrate that amore realistic description of the structure of the intergalactic magnetic fieldis indeed needed. If such a description is adopted, the observational bounds onthe field strength are significantly affected in the limit of short fieldcorrelation lengths: in particular, they acquire a dependence on the magneticfield power spectrum. In the case of intergalactic magnetic fields which aregenerated causally, for which the magnetic field large scale spectral index is$n_B\geq 2$ and even, the observational lower bound becomes more constrainingby about a factor 3. If instead $-3<n_B<-2$, the lower bound is significantlyrelaxed. Such magnetic fields with very red spectra can in principle beproduced during inflation, but remain up to now speculative.

Gamma-ray observations of blazars and the intergalactic magnetic field spectrum