Equivalence of the two results for the free energy of the chiral Potts model
نویسنده
چکیده
The free energy of the chiral Potts model has been obtained in two ways. The first used only the star-triangle relation, symmetries and invariances, and led to a system of equations that implicitly define the free energy, and from which the critical behaviour can be obtained. The second used the functional relations derived by Bazhanov and Stroganov, solving them to obtain the free energy explicitly as a double integral. Here we obtain, for the first time, a direct verification that the two results are identical at all temperatures.
منابع مشابه
Recovery of oil products in Iran by substitution and production effects: A two-stage approach in the form of a general equivalence model
In the energy economics literature, one of the most important approaches to managing energy demand is to improve energy efficiency, which is associated with a concept called a rebound effect. The rebound effect causes the energy saving (due to improved efficiency) to be less than expected. Considering the importance of using oil products in the Iranian economy, the present paper tries to track ...
متن کاملThe “ inversion relation ” method for obtaining the free energy of the chiral Potts model
We derive the free energy of the chiral Potts model by the infinite lattice " inversion relation " method. This method is non-rigorous in that it always needs appropriate analyticity assumptions. Guided by previous calculations based on exact finite-lattice functional relations, we find that in addition to the usual assumption that the free energy be analytic and bounded in some principal domai...
متن کاملThe challenge of the chiral Potts model
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. ...
متن کاملThe Riemann surface of the chiral Potts model free energy function
In a recent paper we derived the free energy or partition function of the N-state chiral Potts model by using the infinite lattice “inversion relation” method, together with a non-obvious extra symmetry. This gave us three recursion relations for the partition function per site Tpq of the infinite lattice. Here we use these recursion relations to obtain the full Riemann surface of Tpq. In terms...
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 2008