Exact Ground State of the Finite-Field Three-State Potts Model on the One-Dimensional Lattice with First and Second Neighbor Interactions

1985 ◽  
Vol 54 (11) ◽  
pp. 4312-4320 ◽  
Author(s):  
Takashi Tonegawa ◽  
Koichi Takasaki ◽  
Makoto Kaburagi
Keyword(s):  
Finite Field ◽  
Potts Model ◽  
Ground State ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Exact Ground State ◽  
The One

THE EFFECT OF A BOND-SITE INTERACTION ON THE GROUND-STATE INSTABILITIES OF THE ONE-DIMENSIONAL HUBBARD MODEL

1995 ◽  
Vol 09 (12) ◽  
pp. 1503-1514 ◽  
Author(s):  
F.D. BUZATU
Keyword(s):  
Hubbard Model ◽  
Ground State ◽  
Temperature Phase ◽  
Zero Temperature ◽  
Perturbative Approach ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Low Concentrations ◽  
The One ◽  
Temperature Phase Diagram

The ground-state instabilities for a one-dimensional lattice system of electrons with onsite (Hubbard) and bond-site (hopping) interactions are analyzed in a perturbative approach. The zero temperature phase diagram at different band fillings is drawn; an attractive (repulsive) bond-site interaction favors the appearance of a superconductor state at low concentrations of electrons (holes). A comparison with the exact results for the Hubbard model and previous works for particular cases is also discussed.

scholarly journals DIFFERENTIAL EQUATION APPROACH FOR ONE- AND TWO-DIMENSIONAL LATTICE GREEN'S FUNCTION

2007 ◽  
Vol 21 (02n03) ◽  
pp. 139-154 ◽  
Author(s):  
J. H. ASAD
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Recurrence Relation ◽  
Green's Function ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
The One ◽  
Lattice Green's Function ◽  
Lattice Green’S Function

A first-order differential equation of Green's function, at the origin G(0), for the one-dimensional lattice is derived by simple recurrence relation. Green's function at site (m) is then calculated in terms of G(0). A simple recurrence relation connecting the lattice Green's function at the site (m, n) and the first derivative of the lattice Green's function at the site (m ± 1, n) is presented for the two-dimensional lattice, a differential equation of second order in G(0, 0) is obtained. By making use of the latter recurrence relation, lattice Green's function at an arbitrary site is obtained in closed form. Finally, the phase shift and scattering cross-section are evaluated analytically and numerically for one- and two-impurities.

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