STATISTICS OF A LINEAR PARAMAGNETIC MACROMOLECULE

1951 ◽  
Vol 29 (3) ◽  
pp. 236-244 ◽  
Author(s):  
W. Opechowski ◽  
J. M. Bryan
Keyword(s):  
Partition Function ◽  
Statistical Mechanics ◽  
Specific Heat ◽  
Low Temperatures ◽  
Paramagnetic Susceptibility ◽  
Physical Systems ◽  
Asymptotic Expressions ◽  
Paramagnetic Atoms

The partition function of a linear "macromolecule" composed of N paramagnetic atoms subject to the Ising interaction is calculated for an arbitrary N. From the partition function the expressions for the specific heat and the initial paramagnetic susceptibility are obtained. It is shown on the example of the susceptibility that the procedure, customary in statistical mechanics, which consists in using the asymptotic expressions (N→∞) to describe actual physical systems (N very large, but finite) should be used with some caution in the region of very low temperatures.

THERMODYNAMICS OF q-MODIFIED BOSONS

1996 ◽  
Vol 10 (06) ◽  
pp. 683-699 ◽  
Author(s):  
P. NARAYANA SWAMY
Keyword(s):  
Mechanical Properties ◽  
Phase Transition ◽  
Equation Of State ◽  
Partition Function ◽  
Statistical Mechanics ◽  
Specific Heat ◽  
Thermodynamic Functions ◽  
Bose Condensation ◽  
Grand Partition Function ◽  
Statistical Mechanical

Based on a recent study of the statistical mechanical properties of the q-modified boson oscillators, we develop the statistical mechanics of the q-modified boson gas, in particular the Grand Partition Function. We derive the various thermodynamic functions for the q-boson gas including the entropy, pressure and specific heat. We demonstrate that the gas exhibits a phase transition analogous to ordinary bose condensation. We derive the equation of state and develop the virial expansion for the equation of state. Several interesting properties of the q-boson gas are derived and compared with those of the ordinary boson which may point to the physical relevance of such systems.

Specific heat of ordered and isotopically disordered lattices

1978 ◽  
Vol 56 (10) ◽  
pp. 1390-1394
Author(s):  
K. P. Srivastava
Keyword(s):  
Specific Heat ◽  
Low Temperatures ◽  
Numerical Study ◽  
Three Dimensional ◽  
Constant Volume ◽  
Nearest Neighbour ◽  
Two Dimensional ◽  
Appreciable Difference ◽  
Substantial Change ◽  
Neighbour Interaction

An extensive numerical study on specific heat at constant volume (Cv) for ordered and isotopically disordered lattices has been made. Cv at various temperatures for ordered and disordered linear and two-dimensional lattices have been compared and no appreciable difference in Cv between these two structures has been observed. Effect of concentration of light atoms on Cv for three-dimensional isotopically disordered lattices has also been shown.In spite of taking next-nearest-neighbour interaction into account, no substantial change in Cv between the ordered and isotopically disordered linear lattices has been found. It is shown that the low lying modes contribute substantially at low temperatures.

Thermal Properties of an Incompletely Degenerate Fermi Gas

1936 ◽  
Vol 32 (1) ◽  
pp. 108-111 ◽  
Author(s):  
N. F. Mott
Keyword(s):  
Thermal Properties ◽  
Specific Heat ◽  
Electron Gas ◽  
Electronic States ◽  
Fermi Gas ◽  
Paramagnetic Susceptibility ◽  
Free Electrons ◽  
Periodic Field ◽  
Degenerate Fermi Gas ◽  
Image Position

The purpose of this note is to calculate the specific heat and paramagnetic susceptibility of an electron gas obeying the Fermi-Dirac statistics for all temperatures, including those temperatures for which the gas is partially degenerate. The results are applicable to the electrons in a metal, whether free or moving in a periodic field, provided only that the number of electronic states per gram atom with energy between E and E + dE can be expressed in the formas for free electrons.

Specific heat of the iron-hydrogen system at low temperatures

1979 ◽  
Vol 13 (7) ◽  
pp. 573-575 ◽  
Author(s):  
Hiroaki Wada ◽  
Koshiro Sakamoto
Keyword(s):  
Specific Heat ◽  
Low Temperatures ◽  
Hydrogen System

Specific heat of single crystal Ba0.6K0.4BiO3 at low temperatures

1996 ◽  
Vol 97 (3) ◽  
pp. 175-178 ◽  
Author(s):  
E.B. Nyeanchi ◽  
D.F. Brewer ◽  
T.E. Hargreaves ◽  
N.E. Hussey ◽  
A.L. Thomson ◽  
...  
Keyword(s):  
Single Crystal ◽  
Specific Heat ◽  
Low Temperatures

Specific Heat Anomalies of PtCo Alloys at Very Low Temperatures

1974 ◽  
pp. 520-524 ◽  
Author(s):  
P. Costa-Ribeiro ◽  
M. Saint-Paul ◽  
D. Thoulouze ◽  
R. Tournier
Keyword(s):  
Specific Heat ◽  
Low Temperatures

scholarly journals Hard Squares with Negative Activity and Rhombus Tilings of the Plane

10.37236/1093 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
Jakob Jonsson
Keyword(s):  
Partition Function ◽  
Statistical Mechanics ◽  
Simplicial Complex ◽  
Transfer Matrix ◽  
Euler Characteristic ◽  
Independent Sets ◽  
Roots Of Unity ◽  
Hard Squares ◽  
Vertex Set

Let $S_{m,n}$ be the graph on the vertex set ${\Bbb Z}_m \times {\Bbb Z}_n$ in which there is an edge between $(a,b)$ and $(c,d)$ if and only if either $(a,b) = (c,d\pm 1)$ or $(a,b) = (c \pm 1,d)$ modulo $(m,n)$. We present a formula for the Euler characteristic of the simplicial complex $\Sigma_{m,n}$ of independent sets in $S_{m,n}$. In particular, we show that the unreduced Euler characteristic of $\Sigma_{m,n}$ vanishes whenever $m$ and $n$ are coprime, thereby settling a conjecture in statistical mechanics due to Fendley, Schoutens and van Eerten. For general $m$ and $n$, we relate the Euler characteristic of $\Sigma_{m,n}$ to certain periodic rhombus tilings of the plane. Using this correspondence, we settle another conjecture due to Fendley et al., which states that all roots of $\det (xI-T_m)$ are roots of unity, where $T_m$ is a certain transfer matrix associated to $\{\Sigma_{m,n} : n \ge 1\}$. In the language of statistical mechanics, the reduced Euler characteristic of $\Sigma_{m,n}$ coincides with minus the partition function of the corresponding hard square model with activity $-1$.

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