Exact Finite Method of Lattice Statistics. II. Honeycomb‐Lattice Gas of Hard Molecules

1967 ◽  
Vol 47 (10) ◽  
pp. 4015-4020 ◽  
Author(s):  
L. K. Runnels ◽  
L. L. Combs ◽  
James P. Salvant
Keyword(s):  
Lattice Gas ◽  
Honeycomb Lattice ◽  
Lattice Statistics ◽  
Finite Method

Exact Finite Method of Lattice Statistics. IV. Square Well Lattice Gas

1970 ◽  
Vol 52 (5) ◽  
pp. 2352-2358 ◽  
Author(s):  
L. K. Runnels ◽  
J. P. Salvant ◽  
H. R. Streiffer
Keyword(s):  
Lattice Gas ◽  
Lattice Statistics ◽  
Square Well ◽  
Finite Method

Stable superstructures in a binary honeycomb-lattice gas

2011 ◽  
Vol 36 (1) ◽  
pp. 1338-1343 ◽  
Author(s):  
Taras M. Radchenko ◽  
Valentyn A. Tatarenko
Keyword(s):  
Lattice Gas ◽  
Honeycomb Lattice

Critical behaviour of the hard-core lattice gas on the honeycomb lattice

1983 ◽  
Vol 97 (6) ◽  
pp. 235-238 ◽  
Author(s):  
Jean-Marc Debierre ◽  
Loîc Turban
Keyword(s):  
Lattice Gas ◽  
Hard Core ◽  
Critical Behaviour ◽  
Honeycomb Lattice

On the cubic lattice Green functions

1994 ◽  
Vol 445 (1924) ◽  
pp. 463-477 ◽  
Keyword(s):  
Basic Result ◽  
Honeycomb Lattice ◽  
Lattice Statistics ◽  
Green Functions ◽  
Cubic Lattice ◽  
Heun Function ◽  
Hypercubic Lattice ◽  
The Face ◽  
Complete Elliptic Integrals ◽  
The Green Function

It is proved that K ( k + ) = [(4 – η ) 1/2 – (1 – η ) 1/2 ] K ( k _), where η is a complex variable which lies in a certain region R 2 of the η plane, and K ( k ± ) are complete elliptic integrals of the first kind with moduli k ± which are given by k 2 ± Ξ k 2 ± ( η ) = 1/2 + 1/4 η (4 – η ) 1/2 – 1/4 (2 – η ) (1 – η ) 1/2 . This basic result is then used to express the face-centred cubic and simple cubic lattice Green functions at the origin in terms of the square of a complete ellip­tic integral of the first kind. Several new identities involving the Heun function are also derived. F(a, b; α,β, γ, δ; η) are also derived. Next it is shown that the three cubic lat­tice Green functions all have parametric representations which involve the Green function for the two-dimensional honeycomb lattice. Finally, the results are ap­plied to a variety of problems in lattice statistics. In particular, a new simplified formula for the generating function of staircase polygons on a four-dimensional hypercubic lattice is derived.

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