aqora

The critical line of an asymmetric eight vertex model

Michael N. Barber, Franz S. Rys

The European Physical Journal BJun 1, 19856 citations

The odd eight-vertex model

Fa Yueh Wu, H. Kunz

We consider a vertex model on the simple-quartic lattice defined by line graphs on the lattice for which there is always an odd number of lines incident at a vertex. This is the odd 8-vertex model which has eight possible vertex configurations. We establish that the odd 8-vertex model is equivalent to a staggered 8-vertex model. Using this equivalence we deduce the solution of the odd 8-vertex model when the weights satisfy a free-fermion condition. It is found that the freefermion model exhibits no phase transitions in the regime of positive vertex weights. We also establish the complete equivalence of the free-fermion odd 8-vertex model with the free-fermion 8-vertex model solved by Fan and Wu. Our analysis leads to several Ising model representations of the free-fermion model with pure 2-spin interactions. Key words: Odd eight-vertex model, free-fermion model, exact solution. 1 2 1We consider a vertex model on the simple-quartic lattice defined by line graphs on the lattice for which there is always an odd number of lines incident at a vertex. This is the odd 8-vertex model which has eight possible vertex configurations. We establish that the odd 8-vertex model is equivalent to a staggered 8-vertex model. Using this equivalence we deduce the solution of the odd 8-vertex model when the weights satisfy a free-fermion condition. It is found that the freefermion model exhibits no phase transitions in the regime of positive vertex weights. We also establish the complete equivalence of the free-fermion odd 8-vertex model with the free-fermion 8-vertex model solved by Fan and Wu. Our analysis leads to several Ising model representations of the free-fermion model with pure 2-spin interactions. Key words: Odd eight-vertex model, free-fermion model, exact solution. 1 2 1

Jan 1, 20082 citations

Analytic theory of the eight-vertex model

Vladimir V. Bazhanov, Vladimir V. Mangazeev

arXiv:hep-th/0609153Nuclear Physics BJan 14, 200734 citations

Universality for the critical lines of the eight-vertex, Ashkin-Teller, and Gaussian models

Adrianus M. M. Pruisken, A. C. Brown

A perturbation expansion has been performed for the critical lines of the eight-vertex and Ashkin-Teller models around the decoupling point. The critical temperature and the details of the mapping of these lines onto the Gaussian-model critical line is calculated to second order in the marginal parameters. We find agreement with the exactly known results for these models and with the mapping formalism of Kadanoff and Brown.

Physical review. B, Condensed matterFeb 1, 198121 citations

New solvable cases for the eight-vertex model

Ingo Peschel, Franz S. Rys

Physics Letters ASep 1, 198218 citations

On the eight-vertex model and related models: A new method and some new results

J. Zittartz

Physica A Statistical Mechanics and its ApplicationsFeb 1, 19901 citation

Sum Rule for the Eight-Vertex Model on Its Combinatorial Line

Related papers

Sum Rule for the Eight-Vertex Model on Its Combinatorial Line

Related papers