  Thermodynamics of the short-range model of spin ice magnets in a field is
considered in the Bethe - Peierls approximation. The results obtained for
[111], [100] and [011] fields agrees reasonably well with the existing
Monte-Carlo simulations and some experiments. In this approximation all
extremely sharp field-induced anomalies are described by the analytical
functions of temperature and applied field. In spite of the absence of true
phase transitions the analysis of the entropy and specific heat reliefs over
H-T plane allows to discern the "pseudo-phases" with specific character of spin
fluctuations and define the lines of more or less sharp "pseudo-transitions"
between them.
