Local three-spin correlations in the free-fermion and planar Ising models

1989 ◽  
Vol 423 (1865) ◽  
pp. 279-300 ◽  
Keyword(s):  
Ising Model ◽  
Ising Models ◽  
Square Lattice ◽  
Free Fermion ◽  
Two Dimensional ◽  
Solvable Models ◽  
Spin Correlations ◽  
Fermion Model ◽  
Free Fermion Model

A number of local three-spin correlations are calculated exactly for various related ferromagnetic two-dimensional solvable models in statistical mechanics.They are the square lattice free-fermion model, the equivalent checkerboard Ising model, and the anisotropic triangular, honeycomb and square lattice Ising models. The different results are all applications of a single unifying formula.

scholarly journals QUANTUM MODEL OF INTERACTING "STRINGS" ON THE SQUARE LATTICE

2000 ◽  
Vol 15 (01) ◽  
pp. 105-131
Author(s):  
H. E. BOOS
Keyword(s):  
Square Lattice ◽  
Quantum Model ◽  
Free Fermion ◽  
Two Dimensional ◽  
Fermion Model ◽  
One Dimensional ◽  
Single String ◽  
Free Fermion Model ◽  
Xy Spin Chain ◽  
The One

The model which is the generalization of the one-dimensional XY-spin chain for the case of the two-dimensional square lattice is considered. The subspace of the "string" states is studied. The solution to the eigenvalue problem is obtained for the single "string" in cases of the "string" with fixed ends and "string" of types (1, 1) and (1, 2) living on the torus. The latter case has the features of a self-interacting system and does not seem to be integrable while the previous two cases are equivalent to the free-fermion model.

Free-fermion, checkerboard and Z -invariant lattice models in statistical mechanics

1986 ◽  
Vol 404 (1826) ◽  
pp. 1-33 ◽  
Keyword(s):  
Ising Model ◽  
Potts Model ◽  
Three Dimensional ◽  
Lattice Models ◽  
Square Lattice ◽  
Free Fermion ◽  
Local Correlations ◽  
Free Fermion Model ◽  
Zamolodchikov Model ◽  
Special Case

It is shown that the two-dimensional free fermion model is equivalent to a checkerboard Ising model, which is a special case of the general ‘ Z -invariant’ Ising model. Expressions are given for the partition function and local correlations in terms of those of the regular square lattice Ising model. Corresponding results are given for the self-dual Potts model, and the application of the methods to the three-dimensional Zamolodchikov model is discussed. The paper ends with a discussion of the critical and disorder surfaces of the checkerboard Potts model.

HIGH-TEMPERATURE SUSCEPTIBILITY SERIES FOR SQUARE-LATTICE ISING MODEL WITH FIRST AND SECOND NEIGHBOUR INTERACTIONS

2002 ◽  
Vol 16 (32) ◽  
pp. 4919-4922
Author(s):  
KEH YING LIN ◽  
MALL CHEN
Keyword(s):  
High Temperature ◽  
Critical Temperature ◽  
Ising Model ◽  
Critical Exponent ◽  
Ising Models ◽  
Temperature Series ◽  
Square Lattice ◽  
Zero Field ◽  
Two Dimensional ◽  
Temperature Susceptibility

We have calculated the high-temperature series expansion of the zero-field susceptibility of the square-lattice Ising model with first and second neighbour interactions to the 20th order by computer. Our results extend the previous calculation by Hsiao and Lin to two more orders. We use the Padé approximants to estimate the critical exponent γ and the critical temperature. Our result 1.747 < γ < 1.753 supports the universality conjecture that all two-dimensional Ising models have the same critical exponent γ = 1.75.

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