scholarly journals ON THE SPECTRUM, NO-GHOST THEOREM AND MODULAR INVARIANCE OF W3 STRINGS

1993 ◽  
Vol 08 (17) ◽  
pp. 2875-2893 ◽  
Author(s):  
PETER WEST
Keyword(s):  
Ising Model ◽  
Partition Function ◽  
Ghost Number ◽  
Modular Invariance ◽  
Modular Invariant

A spectrum-generating algebra is constructed and used to find all the physical states of the W3 string with standard ghost number. These states are shown to have positive norm and their partition function is found to involve the Ising model characters corresponding to the weights 0 and 1/16. The theory is found to be modular invariant if, in addition, one includes states that correspond to the Ising character of weight 1/2. It is shown that these additional states are indeed contained in the cohomology of Q.

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.

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

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.

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