On the Algebraic Approach to Cubic Lattice Potts Models
نویسنده
چکیده
We consider Diagram algebras, DG(Q) (generalized Temperley-Lieb algebras) defined for a large class of graphs G, including those of relevance for cubic lattice Potts models, and study their structure for generic Q. We find that these algebras are too large to play the precisely analogous role in three dimensions to that played by the Temperley-Lieb algebras for generic Q in the planar case. We outline measures to extract the quotient algebra that would illuminate the physics of three dimensional Potts models. PACS: 75.10.H
منابع مشابه
Calculation of the Critical Temperature for 2- and 3-Dimensional Ising Models and for 2-Dimensional Potts Models Using the Transfer Matrix Method
A new graphical method is developed to calculate the critical temperature of 2and 3-dimensional Ising models as well as that of the 2-dimensional Potts models. This method is based on the transfer matrix method and using the limited lattice for the calculation. The reduced internal energy per site has been accurately calculated for different 2-D Ising and Potts models using different size-limit...
متن کاملAn algebraic approach to coarse graining
We propose that Kreimer’s method of Feynman diagram renormalization via a Hopf algebra of rooted trees can be fruitfully employed in the analysis of block spin renormalization or coarse graining of inhomogeneous statistical systems. Examples of such systems include spin foam formulations of non-perturbative quantum gravity as well as lattice gauge and spin systems on irregular lattices and/or w...
متن کامل2 00 3 Introduction to solvable lattice models in statistical and mathematical physics ∗
Some features of integrable lattice models are reviewed for the case of the six-vertex model. By the Bethe ansatz method we derive the free energy of the six-vertex model. Then, from the expression of the free energy we show analytically the critical singularity near the phase transition in the anti-ferroelectric regime, where the essential singularity similar to the Kosterlitz-Thouless transit...
متن کاملAlgebraic Geometry and Physics 1
This article is an interdisciplinary review and an ongoing progress report over the last few years made by myself and collaborators in certain fundamental subjects on two major theoretic branches in mathematics and theoretical physics: algebraic geometry and quantum physics. I shall take a practical approach, concentrating more on explicit examples rather than formal developments. Topics covere...
متن کاملJa n 20 05 Determinant of the Potts model transfer matrix and the critical point
By using a decomposition of the transfer matrix of the q-state Potts Model on a three dimensional m× n× n simple cubic lattice its determinant is calculated exactly. By using the calculated determinants a formula is conjectured which approximates the critical temperature for a d-dimensional hypercubic lattice. PACS numbers: 05.50.+q, 02.70.-c
متن کامل