Thermodynamics of the two-dimensional and three-dimensional Ising models in the static fluctuation approximation

1989 ◽  
Vol 80 (1) ◽  
pp. 736-745 ◽  
Author(s):  
R. R. Nigmatullin ◽  
V. A. Toboev
Keyword(s):  
Three Dimensional ◽  
Ising Models ◽  
Two Dimensional ◽  
Static Fluctuation Approximation ◽  
Static Fluctuation

The temperature and frequency dependence of the inelastic neutron scattering from an Ising magnet

1968 ◽  
Vol 46 (7) ◽  
pp. 799-802 ◽  
Author(s):  
G. A. T. Allan ◽  
D. D. Betts
Keyword(s):  
Inelastic Scattering ◽  
Inelastic Neutron Scattering ◽  
Three Dimensional ◽  
Ising Models ◽  
Inelastic Neutron ◽  
Square Lattice ◽  
Two Dimensional ◽  
Scattering Function ◽  
Ising Magnet ◽  
Exact Energy

The magnetic inelastic scattering of neutrons from a spin-[Formula: see text] Ising system is considered. For the two-dimensional plane square lattice, the exact energy distribution of the scattering is obtained at all temperatures. It consists of a number of discrete levels, the envelope of which varies most markedly in the critical region. Some qualitative projections are also made concerning three-dimensional systems. For both two- and three-dimensional Ising models there can be no wave-vector dependence of the inelastic scattering function because there is correlation only between z components of the spins on different sites.

scholarly journals Thermodynamic properties of graphene using the static fluctuation approximation (SFA)

2017 ◽  
Vol 95 (3) ◽  
pp. 211-219 ◽  
Author(s):  
Mustafa M. Hawamdeh ◽  
Mohamed K. Al-Sugheir ◽  
Ayman S. Sandouqa ◽  
Humam B. Ghassib
Keyword(s):  
Thermodynamic Properties ◽  
Statistical Mechanics ◽  
Ideal Gas ◽  
Two Dimensional ◽  
Nonextensive Statistical Mechanics ◽  
Static Fluctuation Approximation ◽  
Entropy Parameter ◽  
The Mean ◽  
Static Fluctuation ◽  
Good Agreement

The thermodynamic properties of two-dimensional graphene nanosystems are investigated using the static fluctuation approximation (SFA). These properties are analyzed using both extensive and nonextensive statistical mechanics. It is found that these properties are less sensitive to temperature when using nonextensive — in contrast to extensive — statistical mechanics. It is also noted that the mean internal energy and the specific heat behave as a power law, Tα, at T < 8 eV; whereas they go to the classical limit for the two-dimensional ideal gas at T > 8 eV. The results are presented in a set of figures and one table. The roles played by the number of particles and the entropy parameter q are underlined. Whenever possible, comparisons are made to previous studies. It is concluded that Boltzmann–Gibbs statistics are not valid for some cases, and that SFA results are in good agreement with those obtained within other formalisms.

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