Reasonable and robust Hamiltonians violating the third law of thermodynamics

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 55, Issue 6, 1997, Pages 6459-6466

  Watson, Greg ^a   Canright, Geoff ^b,c   Somer, Frank L ^a  

^a RUTHERFORD APPLETON LABORATORY   (United Kingdom)

^b UNIVERSITY OF TENNESSEE   (United States)

^c OAK RIDGE NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0006387024     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.56.6459     Document Type: Article

References (16)

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12. Consider the polytope (Formula presented), formed of the convex combinations of (Formula presented) and its neighbors. Then there is a convex polytope (Formula presented) in the neighborhood of (Formula presented) in which the two polytopes (Formula presented) and (Formula presented) are indistinguishable;see G. M. Ziegler, Lectures on Polytopes, Graduate Texts in Mathematics Vol. 152 (Springer, Berlin, 1995). Now if (Formula presented) is not a neighbor of (Formula presented), then (Formula presented) exits (Formula presented) at some point that is not a vertex of (Formula presented). Hence the intersection (Formula presented) of (Formula presented) with (Formula presented) may be written as a linear combination of the edge vectors (Formula presented), (Formula presented), with non-negative coefficients, at least two being nonzero. Extending this result (by extending the vectors) gives Eq. (4). Our lemma 1 is encountered, in a different form, in the mathematics of the simplex algorithm of linear programming.
13. J. Yi and G. S. Canright, Phys. Rev. B 53, 5198 (1996).PRBMDO
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