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Electrocaloric effect in KH$_2$PO$_4$

The proton ordering model for the KH$_{2}$PO$_{4}$ type ferroelectrics is modified by taking into account non-linear effects, namely, the dependence of the effective dipole moments on the proton ordering parameter. Within the four-particle cluster approximation we calculate the crystal polarization, longitudinal dielectric permittivity, specific heat, and explore the electrocaloric effect. Smearing of the ferroelectric phase transition by the longitudinal electric field is described. A good agreement with experiment is obtained.