On the low-temperature behavior of the critical specific heat capacity of an anharmonic crystal with long-range interaction

Pisanova, E. S.; Krushkov, Angel Y.

doi:10.1063/1.4944248

Cited by 1 publication

(6 citation statements)

References 7 publications

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“…where ∆ 0 is the solution of the self-consistent equation ( 9). Since for t > t c , near the critical point, the solution ∆ 0 of equation ( 9) decreases when t decreases, and ∆ 0 = 0 for all temperatures t ≤ t c , then the specific heat capacity (11) has a cusp-type singularity at the critical temperature t c and keeps its maximum value c max = 1 for all t ≤ t c . A similar critical behavior of the specific heat capacity with c max = 1/2 has been found within the mean spherical model in [1].…”

Section: The Critical Specific Heat Capacity Of a Classical Systemmentioning

confidence: 99%

“…The result (11) has been obtained in [12], where the critical specific heat capacity of a 2σ-dimensional classical system at t > t c has been expressed in the Lambert W-function terms.…”

Section: The Critical Specific Heat Capacity Of a Classical Systemmentioning

confidence: 99%

“…To obtain the leading critical behavior of the specific heat capacity (11) for σ < d < 2σ, it is necessary to obtain the corresponding solution ∆ 0 of equation ( 9).…”

Section: The Critical Specific Heat Capacity Of a Classical Systemmentioning

confidence: 99%

“…From equations ( 14) and (11), neglecting the small ∆ 0 -term in the brackets in equation ( 11) and introducing the notation…”

Section: The Case σ < D < 2σmentioning

confidence: 99%

“…The bulk critical specific heat capacity of the model has been studied in the cases of a quantum system at low temperatures for d = σ and a classical system for d = 2σ in [11] and [12], respectively.…”

Section: Introductionmentioning

confidence: 99%

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On the classical critical behavior of the specific heat capacity of a model of structural phase transitions with a long-range interaction

Pisanova

2023

J. Phys.: Conf. Ser.

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The critical specific heat capacity c of a d-dimensional model describing structural phase transitions in an anharmonic crystal with a long-range interaction (decreasing at large distances r as r −d−σ , 0 < σ ≤ 2) is studied near the classical critical point Tc . At temperatures T > Tc and for dimensions σ < d < 2σ (σ and 2σ are the lower and the upper critical dimensions, respectively) the critical specific heat capacity is obtained in the form c ≈ 1 − Dεαs , where D > 0 and αs < 0 depend only on the ratio d/σ, and ε = T/Tc −1 is a measure of the deviation from the critical point. For three fixed values of the ratio d/σ the dependence c ≈ c(ε) is graphically presented. It is shown that at all temperatures T ≤ Tc the specific heat capacity retains its maximum value, c max = 1. The critical exponent αs , obtained here, coincides with that of the known mean spherical model, while c max is different for the two models.

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Section: The Critical Specific Heat Capacity Of a Classical Systemmentioning

confidence: 99%

“…The result (11) has been obtained in [12], where the critical specific heat capacity of a 2σ-dimensional classical system at t > t c has been expressed in the Lambert W-function terms.…”

Section: The Critical Specific Heat Capacity Of a Classical Systemmentioning

confidence: 99%

“…To obtain the leading critical behavior of the specific heat capacity (11) for σ < d < 2σ, it is necessary to obtain the corresponding solution ∆ 0 of equation ( 9).…”

Section: The Critical Specific Heat Capacity Of a Classical Systemmentioning

confidence: 99%

“…From equations ( 14) and (11), neglecting the small ∆ 0 -term in the brackets in equation ( 11) and introducing the notation…”

Section: The Case σ < D < 2σmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On the classical critical behavior of the specific heat capacity of a model of structural phase transitions with a long-range interaction

Pisanova

2023

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

show abstract

On the low-temperature behavior of the critical specific heat capacity of an anharmonic crystal with long-range interaction

Cited by 1 publication

References 7 publications

On the classical critical behavior of the specific heat capacity of a model of structural phase transitions with a long-range interaction

On the classical critical behavior of the specific heat capacity of a model of structural phase transitions with a long-range interaction

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