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pro vyhledávání: '"Baxter, R. J."'
Autor:
Baxter, R. J.
Publikováno v:
Proc. Roy. Soc. A 476: 20190713 (2020) 18 pages
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 serie
Externí odkaz:
http://arxiv.org/abs/1909.00518
Autor:
Baxter, R. J.
Publikováno v:
J. Phys. A:math. Theor. 50 (2017) 014001 (40pp)
We use Kaufman's spinor method to calculate the bulk, surface and corner free energies $f_b, f_s, f_s', f_c$ of the anisotropic square lattice zero-field Ising model for the ordered ferromagnetic case. For $f_b, f_s, f'_s$ our results of course agree
Externí odkaz:
http://arxiv.org/abs/1606.02029
Autor:
Baxter, R. J.
We consider the bulk, vertical surface, horizontal surface and corner free energies $f_b, f_s, f'_s, f_c$ of the anisotropic self-dual $Q$-state Potts model for $Q > 4$. $f_b$ was calculated in 1973[1]. For $Q<4$, $f_s, f'_s$ were calculated in 1989[
Externí odkaz:
http://arxiv.org/abs/1606.01616
Autor:
Baxter, R. J.
Publikováno v:
J. Phys. A 47, 315001 (2014) (12 pages)
Paul Fendley has recently found a "parafermionic" way to diagonalise a simple solvable hamiltonian associated with the chiral Potts model. Here we indicate how this method generalizes to the $\tau_2$ model with open boundaries and make some comments.
Externí odkaz:
http://arxiv.org/abs/1310.7074
Autor:
Baxter, R. J.
Publikováno v:
J. Stat.Phys. 149, 1164 --1167 (2012)
In 2011 I reviewed the calculation by Onsager and Kaufman of the spontaneous magnetization of the square-lattice Ising model, which Onsager announced in 1949 but never published. I have recently been alerted to further original papers that bear on th
Externí odkaz:
http://arxiv.org/abs/1211.2665
Autor:
Baxter, R. J.
Publikováno v:
J. Stat. Phys. 145:518-548 (2011)
Lars Onsager announced in 1949 that he and Bruria Kaufman had proved a simple formula for the spontaneous magnetization of the square-lattice Ising model, but did not publish their derivation. It was three years later when C. N. Yang published a deri
Externí odkaz:
http://arxiv.org/abs/1103.3347
Autor:
Baxter, R. J.
Publikováno v:
J. Stat. Mech. P11037 (26 pages) (2010)
Lars Onsager and Bruria Kaufman calculated the partition function of the Ising model exactly in 1944 and 1949. Since then there have been many developments in the exact solution of similar, but usually more complicated, models. Here I shall mention a
Externí odkaz:
http://arxiv.org/abs/1010.0710
Autor:
Baxter, R. J.
Publikováno v:
ANZIAM, volume 51, pages 309 -316 (2010)
The superintegrable chiral Potts model has many resemblances to the Ising model, so it is natural to look for algebraic properties similar to those found for the Ising model by Onsager, Kaufman and Yang. The spontaneous magnetization M_r can be writt
Externí odkaz:
http://arxiv.org/abs/1001.0281
Autor:
Baxter, R. J.
Publikováno v:
J. Phys. A Math. Theor. 43, 145002 (16 pages) (2010)
For the Ising model, the calculation of the spontaneous magnetization leads to the problem of evaluating a determinant. Yang did this by calculating the eigenvalues in the large-lattice limit. Montroll, Potts and Ward expressed it as a Toeplitz deter
Externí odkaz:
http://arxiv.org/abs/0912.4549
Autor:
Baxter, R. J.
Publikováno v:
J. Stat. Phys. 137, 798 - 813 (2009)
The spontaneous magnetization of a two-dimensional lattice model can be expressed in terms of the partition function $W$ of a system with fixed boundary spins and an extra weight dependent on the value of a particular central spin. For the superinteg
Externí odkaz:
http://arxiv.org/abs/0906.3551