Violating of the classical Essam-Fisher and Rushbrooke formulas for quantum phase transitions

TL;DR

This paper demonstrates that classical critical exponent relations do not hold for quantum phase transitions at zero temperature, proposing a generalized formula applicable across all dimensions that aligns with experimental data.

Contribution

It introduces a generalized formula for critical exponents in quantum phase transitions, extending classical relations to zero-temperature cases and clarifying experimental observations.

Findings

Classical Essam-Fisher and Rushbrooke formulas are invalid at zero critical temperature.

A new general formula for critical exponents in quantum PTs is proposed.

The theory's predictions match experimental data without challenging the scaling hypothesis.

Abstract

The classical Essam-Fisher and Rushbrooke relationships (1963) that connect the equilibrium critical exponents of susceptibility, specific heat and order parameter are shown to be valid only if the critical temperature is positive. For quantum phase transitions (PT) with zero critical temperature, 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 of any space dimension. The predictions of the theory are consistent with the available experimental data and do not cast any doubts upon the scaling hypothesis.