Critical properties of the hierarchical reference theory: Further investigations

Høye, Johan S.; Lomba, Enrique

doi:10.1016/j.molliq.2018.01.001

Cited by 2 publications

(3 citation statements)

References 34 publications

(36 reference statements)

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“…With SCOZA, β is replaced by an effective inverse temperature as a free parameter to be determined via thermodynamic self-consistency between the internal energy and compressibility. Again, very accurate results came out, also in the critical region, and various generalizations have been dealt with …”

Section: Other Approachesmentioning

confidence: 95%

“…It was found that the HRT critical indices were simple rational numbers. By direct investigation of the HRT partial differential equation using both analytical and numerical methods, the critical properties of HRT were also determined by the solution of a transformed HRT partial differential equation that was expanded in leading and subleading scaling contributions that fulfill ordinary differential equations. These contributions are connected via simple powers of the cutoff parameter of renormalization, leading again to simple rational numbers for the critical exponents.…”

Section: Other Approachesmentioning

confidence: 99%

“…Again, very accurate results came out, also in the critical region, and various generalizations have been dealt with. 713 A unification of HRT and SCOZA was made by Høye and Reiner 714,715 and further analyzed in the critical region 716 where the two free parameters were found to be essentially determined by the sum of the HRT and SCOZA problems. Since these two theories qualitatively have somewhat different critical behaviors, the problem to reconcile them implied the presence of subleading scaling terms.…”

Section: Two-phase Approachesmentioning

confidence: 99%

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Melting Is Well-Known, but Is It Also Well-Understood?

de With

2023

Chem. Rev.

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Contrary to continuous phase transitions, where renormalization group theory provides a general framework, for discontinuous phase transitions such a framework seems to be absent. Although the thermodynamics of the latter type of transitions is wellknown and requires input from two phases, for melting a variety of one-phase theories and models based on solids has been proposed, as a generally accepted theory for liquids is (yet) missing. Each theory or model deals with a specific mechanism using typically one of the various defects (vacancies, interstitials, dislocations, interstitialcies) present in solids. Furthermore, recognizing that surfaces are often present, one distinguishes between mechanical or bulk melting and thermodynamic or surface-mediated melting. After providing the necessary preliminaries, we discuss both types of melting in relation to the various defects. Thereafter we deal with the effect of pressure on the melting process, followed by a discussion along the line of type of materials. Subsequently, some other aspects and approaches are dealt with. An attempt to put melting in perspective concludes this review.

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Section: Other Approachesmentioning

confidence: 95%

Section: Other Approachesmentioning

confidence: 99%