High temperature susceptibility bounds for the two-dimensional Ising model

1972 ◽  
Vol 39 (5) ◽  
pp. 357-358 ◽  
Author(s):  
D.B. Abraham
Keyword(s):  
High Temperature ◽  
Ising Model ◽  
Two Dimensional ◽  
Temperature Susceptibility

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.

The Grassmann Representation of Ising Model

1998 ◽  
Vol 12 (20) ◽  
pp. 1995-2003 ◽  
Author(s):  
K. Nojima
Keyword(s):  
High Temperature ◽  
Ising Model ◽  
Ising Models ◽  
Integral Representations ◽  
Dimensional Case ◽  
Partition Functions ◽  
Fermion Field ◽  
Two Dimensional

The integral representations for the partition functions of Ising models are surveyed. The connection with the underlying fermion field in the two-dimensional case is discussed. The relation between the low and the high-temperature expansions is examined.

Duality of the Two-dimensional Ising Model

2020 ◽  
pp. 161-188
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Phase Transition ◽  
High Temperature ◽  
Ising Model ◽  
Statistical Models ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Duality Transformations ◽  
Peierls Argument ◽  
Chapter Deal ◽  
Sum Formula

Chapter 4 begins by discussing the Peierls argument, which allows us to prove the existence of a phase transition in the two-dimensional Ising model. The remaining sections of the chapter deal with duality transformations (duality in square, hexagonal and triangular lattices) that link the low- and high-temperature phases of several statistical models. Particularly important is the proof of the so-called star-triangle identity. This identity will be crucial in the later discussion of the transfer matrix of the Ising model. Finally, it covers the aspect of duality in two dimensions. An appendix provides information about the Poisson sum formula.

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