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

Vladimir Udodov^*

Department of Theoretical Physics, Katanov Khakas State University, Abakan, Russia.

DOI: 10.4236/wjcmp.2015.52008                

Abstract

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 T_С > 0 and T → T_C. For phase transitions (PT’s) with T_C = 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 T_C = 0 and T_C > 0. The predictions of the theory are consistent with the available experimental data and do not cast any doubts upon the scaling hypothesis.

Keywords

Essam-Fisher and Rushbrooke Relationships, The Equilibrium Critical Exponents, The Scaling Hypothesis, Low Temperatures

Conflicts of Interest

The authors declare no conflicts of interest.

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