scholarly journals Some new results on Yang-Lee zeros of the Ising model partition function

1996 ◽  
Vol 215 (5-6) ◽  
pp. 271-279 ◽  
Author(s):  
Victor Matveev ◽  
Robert Shrock
Keyword(s):  
Ising Model ◽  
Partition Function

scholarly journals The bulk, surface and corner free energies of the anisotropic triangular Ising model

2020 ◽  
Vol 476 (2234) ◽  
pp. 20190713
Author(s):  
Rodney J. Baxter
Keyword(s):  
Free Energy ◽  
Ising Model ◽  
Partition Function ◽  
Temperature Series ◽  
Isotropic Case ◽  
Series Expansions ◽  
Exact Results ◽  
Free Energies ◽  
Bulk Surface ◽  
Bulk Free Energy

We consider the anisotropic Ising model on the triangular lattice with finite boundaries, and use Kaufman’s spinor method to calculate low-temperature series expansions for the partition function to high order. From these, we can obtain 108-term series expansions for the bulk, surface and corner free energies. We extrapolate these to all terms and thereby conjecture the exact results for each. Our results agree with the exactly known bulk-free energy and with Cardy and Peschel’s conformal invariance predictions for the dominant behaviour at criticality. For the isotropic case, they also agree with Vernier and Jacobsen’s conjecture for the 60 ° corners.

Finite Lattice Calculations on Discrete Models

2006 ◽  
Vol 3 (2) ◽  
pp. 296-300
Author(s):  
M. J. Velgakis
Keyword(s):  
Ising Model ◽  
Partition Function ◽  
Finite Lattice ◽  
Nearest Neighbors ◽  
Discrete Models ◽  
New Method ◽  
Stat Phys ◽  
Power Demand ◽  
Lattice Calculations ◽  
Computer Power

A new method is proposed for the calculation of the exact partition function for Ising-like systems, based on finite-lattice arguments. In a way, the method is originated with the finite scaling theories presented by Bhanot [J. Stat. Phys. 60, 55 (1990)] and earlier by Binder [Physica 62, 508 (1972)]. The method is tested on a 2D Ising model with nearest- and next-nearest-neighbors interactions. An asset of the method is the low computer power demand.

scholarly journals STAR-MATRIX MODELS

1995 ◽  
Vol 10 (35) ◽  
pp. 2709-2725
Author(s):  
E. VINTELER
Keyword(s):  
Ising Model ◽  
Partition Function ◽  
Matrix Models ◽  
Critical Behavior ◽  
Gaussian Model ◽  
Explicit Formulas ◽  
Special Cases ◽  
Q Matrix

The star-matrix models are difficult to solve due to the multiple powers of the Vandermonde determinants in the partition function. We apply to these models a modified Q-matrix aprpoach and we get results consistent with those obtained by other methods. As examples we study the inhomogeneous Gaussian model on Bethe tree and matrix q-Potts-like model. For the last model in the special cases q=2 and q=3, we write down explicit formulas which determine the critical behavior of the system. For q=2 we argue that the critical behavior is indeed that of the Ising model on the ϕ3 lattice.

A reformulation of the dimer problem

1968 ◽  
Vol 46 (15) ◽  
pp. 1681-1684 ◽  
Author(s):  
R. W. Gibberd
Keyword(s):  
Ising Model ◽  
Partition Function ◽  
Green’S Function ◽  
Green's Function ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Function Technique ◽  
Value Of Time ◽  
Expectation Value

It is shown that the partition function of the generalized dimer problem can be formulated in terms of a vacuum-to-vacuum expectation value of time-ordered operators. This expression is then evaluated by using Green's function technique, which has already been used in conjunction with the Ising model and ferroelectric problem.

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