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Spectral density of quantum Ising model in two fields for large but finitenumber of spins $N$, is discussed in detail. When all coupling constants are ofthe same order, spectral densities in the bulk are well approximated by aGaussian function which is typical behaviour for many-body models withshort-range interactions. The main part of the paper is devoted to theinvestigation of a different characteristic case when spectral densities havepeaks related with strong degeneracies of unperturbed states in certain limitsof coupling constants. In the strict limit $N\to\infty$, peaks overlap anddisappear but for values of $N$ accessible in numerical calculations they oftenstrongly influence spectral densities and other quantities as well. A simplemethod is developed which permits to find general approximation formulae formulti-peak structure of spectral density in good agreement with numerics.

Spectral density of the quantum Ising model in two fields: Gaussian and multi-Gaussian approximations