Duality relations for the correlation functions of $n$ sites on the boundary of a planar lattice are derived for the $(N_α, N_β)$ model of Domany and Riedel for $n=2,3$ . Our result holds for arbitrary lattices which can have nonuniform interactions.Duality relations for the correlation functions of $n$ sites on the boundary of a planar lattice are derived for the $(N_α, N_β)$ model of Domany and Riedel for $n=2,3$. Our result holds for arbitrary lattices which can have nonuniform interactions.

arXiv:cond-mat/9712111Dec 10, 19970 citations

Lectures on correlation functions

Alexander L. Fetter

Lecture notes in physicsJan 1, 19832 citations

Constraints on Beta Functions from Duality

P.H. Damgaard, Peter E. Haagensen

We analyze the way in which duality constrains the exact beta function and correlation length in single-coupling spin systems. A consistency condition we propose shows very concisely the relation between self-dual points and phase transitions, and implies that the correlation length must be duality invariant. These ideas are then tested on the 2-d Ising model, and used towards finding the exact beta function of the q-state Potts model. Finally, a generic procedure is given for identifying a duality symmetry in other single-coupling models with a continuous phase transition.We analyze the way in which duality constrains the exact beta function and correlation length in single-coupling spin systems. A consistency condition we propose shows very concisely the relation between self-dual points and phase transitions, and implies that the correlation length must be duality invariant. These ideas are then tested on the 2-d Ising model, and used towards finding the exact beta function of the q-state Potts model. Finally, a generic procedure is given for identifying a duality symmetry in other single-coupling models with a continuous phase transition.

Jan 1, 199712 citations

Constraints on beta functions from duality

Poul H Damgaard, Peter E. Haagensen

We analyse the way in which duality constrains the exact beta function and correlation length in single-coupling spin systems. We propose a consistency condition which shows very concisely the relation between self-dual points and phase transitions, and implies that the correlation length must be duality invariant. These ideas are then tested on the two-dimensional Ising model, and used towards finding the exact beta function of the q-state Potts model. Finally, a generic procedure is given for identifying a duality symmetry in other single-coupling models with a continuous phase transition.We analyse the way in which duality constrains the exact beta function and correlation length in single-coupling spin systems. We propose a consistency condition which shows very concisely the relation between self-dual points and phase transitions, and implies that the correlation length must be duality invariant. These ideas are then tested on the two-dimensional Ising model, and used towards finding the exact beta function of the q-state Potts model. Finally, a generic procedure is given for identifying a duality symmetry in other single-coupling models with a continuous phase transition.

arXiv:cond-mat/9609242Journal of Physics A Mathematical and GeneralJul 7, 199713 citations

Correlation duality relations for the (

N_α, N_β

) model

Duality relations for the correlation functions of

n

sites on the boundary of a planar lattice are derived for the

(N_α, N_β)

model of Domany and Riedel for

n=2,3

. Our result holds for arbitrary lattices which can have nonuniform interactions.