Linear chain approximation as the zeroth approximation of the renormalized high density expansion method for quasi-low-dimensional Ising systems

1987 ◽  
Vol 124 (9) ◽  
pp. 485-488 ◽  
Author(s):  
Z. Onyszkiewicz
Keyword(s):  
Linear Chain ◽  
Expansion Method ◽  
High Density ◽  
Zeroth Approximation ◽  
Ising Systems ◽  
Low Dimensional ◽  
Chain Approximation ◽  
Density Expansion

HIGH-DENSITY EXPANSION FOR THE SPINLESS FERMION MODEL II: SECOND AND THIRD ORDER IN 1/z

1988 ◽  
Vol 02 (03n04) ◽  
pp. 521-536 ◽  
Author(s):  
M. BARTKOWIAK ◽  
P. MÜNGER ◽  
K. A. CHAO
Keyword(s):  
Lattice Gas ◽  
Preceding Paper ◽  
Expansion Method ◽  
Quantum Spin ◽  
High Density ◽  
Thermodynamic Quantities ◽  
Approximate Methods ◽  
Fermion Model ◽  
Spinless Fermion ◽  
Density Expansion

The selfconsistent high-density expansion for thermodynamic quantities of the quantum spin-polarized fermion lattice gas, derived in the preceding paper, is extended to higher orders. The (1/z)2 terms in the free energy are evaluated by summing two-loop diagrams and the corresponding equation for critical temperature in the classical limit is discussed. Ground state phase diagram of the system for arbitrary electron density is derived in the first and second order of the expansion. Properties of the half-filled, one-dimensional spinless fermion model at T = 0, obtained here in the first three orders in 1/z, are compared with the results of exact calculations and of other approximate methods. This provides a test for the unrenormalized high-density expansion method.

HIGH-DENSITY EXPANSION FOR THE SPINLESS FERMION MODEL I: FIRST ORDER IN 1/z AND HORWITZ-CALLEN RENORMALIZATION

1988 ◽  
Vol 02 (03n04) ◽  
pp. 483-520 ◽  
Author(s):  
M. BARTKOWIAK ◽  
P. MÜNGER ◽  
R. MICNAS
Keyword(s):  
Three Dimensional ◽  
Charge Ordering ◽  
High Density ◽  
Fermion Model ◽  
First Order ◽  
Diagrammatic Technique ◽  
Spinless Fermion ◽  
Density Expansion ◽  
Band Case ◽  
Second Order Phase Transition

A diagrammatic technique for Hubbard's operators is employed to perform systematically the high-density expansion for the three-dimensional spinless fermion model. The molecular field theory is obtained by the zero-order renormalization of blocks. Summation of the first order diagrams is carried out in both selfconsistent and correctional way. It turns out that the charge ordering parameter, calculated self-consistently, has a jump for a certain medial temperature. We have also shown, that the Horwitz-Callen renormalization leads to the first or second order phase transition, depending on t/W and fails when this ratio is large enough. The phase diagrams of the system for the half-filled band case, derived in both unrenormalized and renormalized first order of high-density expansion are presented.

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