Journal ArticleDOI
Monomers and Dimers
Ole J. Heilmann,Elliott H. Lieb +1 more
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In this paper, it was shown that the free energy of an arbitrary monomer-dimer system is analytic in the density and temperature for nonzero density, and hence that the system has no phase transition.Abstract:
We prove that the free energy of an arbitrary monomer-dimer system is analytic in the density and temperature for nonzero density, and hence that the system has no phase transition. This result can also be used to locate the z =e 2sh roots of the Heisenberg ferromagnet or antiferromagnet at high temperature.read more
Citations
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Journal ArticleDOI
Aromaticity of polycyclic conjugated hydrocarbons.
TL;DR: Theoretical Approach to Chemical Structure, Approximate Approaches versus Ambitious Computations, and Use of Signed Matrices.
Journal ArticleDOI
Theory of monomer-dimer systems
Ole J. Heilmann,Elliott H. Lieb +1 more
TL;DR: In this article, it was shown that no monomer-dimer system can have a phase transition as a function of monomer density except, possibly, when the monomerdensity is minimal (i.e., x = 0).
Journal ArticleDOI
On some counting polynomials in chemistry
TL;DR: Various counting polynomials suggested by chemical and physical problems are discussed and Mathematical relations among them and physico-chemical interpretations are given.
Journal ArticleDOI
Heaps of Pieces, I: Basic Definitions and Combinatorial Lemmas
TL;DR: In this article, the authors introduce the combinatorial notion of heaps of pieces, which gives a geometric interpretation of the Cartier-Foata's commutation monoid, and show that heaps may bring new light on classical subjects as poset theory.
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On the theory of the matching polynomial
Chris Godsil,Ivan Gutman +1 more
TL;DR: This paper reports on the properties of the matching polynomial α(G) of a graph G, and presents a number of recursion formulas from which it follows that many families of orthogonal polynomials arise as matches of suitable families of graphs.
References
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Journal ArticleDOI
Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising Model
T.D. Lee,Chen Ning Yang +1 more
TL;DR: In this paper, the problems of an Ising model in a magnetic field and a lattice gas are proved mathematically equivalent, and an example of a two-dimensional lattice model is given for which the phase transition regions in the $p\ensuremath{-}v$ diagram is exactly calculated.
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On the Dimer Solution of Planar Ising Models
TL;DR: In this paper, the partition function of the Ising model on a general planar lattice was simplified by constructing a lattice LΔ (the ''terminal lattice'' derived from an expanded lattice of L) for which the allowed dimer configurations are in one-one correspondence with allowed Ising polygon configurations on L, and which is planar if L is a planar so that Kasteleyn's theorem may be used directly to construct the appropriate Pfaffian.
Journal ArticleDOI
An attempt to extend the statistical theory of perfect solutions
R. H. Fowler,G. S. Rushbrooke +1 more