The challenge of the chiral Potts model
نویسنده
چکیده
The chiral Potts model continues to pose particular challenges in statistical mechanics: it is “exactly solvable” in the sense that it satisfies the Yang-Baxter relation, but actually obtaining the solution is not easy. Its free energy was calculated in 1988 and the order parameter was conjectured in full generality a year later. However, a derivation of that conjecture had to wait until 2005. Here we discuss that derivation.
منابع مشابه
Finite-size Transfer Matrix of Chiral Potts Model with Alternating Rapidities
We establish the Bethe equation of the τ -model in the N -state chiral Potts model (including the degenerate selfdual cases) with alternating vertical rapidities. The eigenvalues of a finite-size transfer matrix of the chiral Potts model are computed by use of functional relations. The significance of the ”alternating superintegrable” case of the chiral Potts model is discussed, and the degener...
متن کاملDuality and Symmetry in Chiral Potts Model
We discover a Ising-type duality in the general N -state chiral Potts model, which is the Kramers-Wannier duality of planar Ising model when N = 2. This duality relates the spectrum and eigenvectors of one chiral Potts model at a low temperature (of small k) to those of another chiral Potts model at a high temperature (of k). The τ -model and chiral Potts model on the dual lattice are establish...
متن کامل2 9 M ay 2 00 5 The Onsager Algebra Symmetry of τ ( j ) - matrices in the Superintegrable Chiral Potts Model
We demonstrate that the τ (j)-matrices in the superintegrable chiral Potts model possess the Onsager algebra symmetry for their degenerate eigenvalues. The Fabricius-McCoy comparison of functional relations of eight-vertex model for roots of unity and superintegrable chiral Potts model has been carefully analyzed by identifying equivalent terms in the corresponding equations , by which we extra...
متن کاملThree-state chiral Potts models on the triangular lattice: a Monte Carlo study
The q-state chiral Potts model can describe systems that exhibit rich phase diagrams (see, for instance, ref. [l]) and interesting physical properties like commensurate-incommensurate transitions [2]. The chiral Potts model has been extensively studied in the last few years from the point of view of exactly solvable models. Au-Yang et al. discovered integrable cases for the q-state chiral Potts...
متن کاملFinite-size energy levels of the superintegrable chiral Potts model
In the solution of the superintegrable chiral Potts model special polynomials related to the representation theory of the Onsager algebra play a central role. We derive approximate analytic formulae for the zeros of particular polynomials which determine sets of low-lying energy eigenvalues of the chiral Potts quantum chain. These formulae allow the analytic calculation of the leading finite-si...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005