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The Essam-Fisher and Rushbrooke relationships (1963) that connect the equilibrium critical exponents of susceptibility, specific heat and order parameter (and some other relations that follow from the scaling hypothesis) are shown to be valid only if the critical temperature TС > 0 and T → TC. For phase transitions (PT’s) with TC = 0 K these relations are proved to be of different form. This fact has been actually observed experimentally, but the reasons were not quite clear. A general formula containing the classical results as a special case is proposed. This formula is applicable to all equilibrium PT’s of any space dimension for both TC = 0 and TC > 0. The predictions of the theory are consistent with the available experimental data and do not cast any doubts upon the scaling hypothesis.

Violating of the Essam-Fisher and Rushbrooke Relationships at Low Temperatures