Ising correlations and elliptic determinants

Details Ising correlations and elliptic determinants Ising correlations and elliptic determinants

2010-12-13

arxiv.org/abs/1012.2856v2

J. Stat. Phys. 143, (2011), 33-59

Physics

Mathematical Physics

31 pages; v2: added references, final version to appear in J. Stat. Phys

Scientific paper

10.1007/s10955-011-0154-6

Correlation functions of the two-dimensional Ising model on the periodic lattice can be expressed in terms of form factors - matrix elements of the spin operator in the basis of common eigenstates of the transfer matrix and translation operator. Free-fermion structure of the model implies that any multiparticle form factor is given by the pfaffian of a matrix constructed from the two-particle ones. Crossed two-particle form factors can be obtained by inverting a block of the matrix of linear transformation induced on fermions by the spin conjugation. We show that the corresponding matrix is of elliptic Cauchy type and use this observation to solve the inversion problem explicitly. Non-crossed two-particle form factors are then obtained using theta functional interpolation formulas. This gives a new simple proof of the factorized formulas for periodic Ising form factors, conjectured by A. Bugrij and one of the authors.

Affiliated with

Also associated with

No associations

Rating

Ising correlations and elliptic determinants does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Ising correlations and elliptic determinants, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Ising correlations and elliptic determinants will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-177770