# The Ising correlation $C(M,N)$ for $\nu=-k$

@article{Boukraa2020TheIC, title={The Ising correlation \$C(M,N)\$ for \$\nu=-k\$}, author={Salah Boukraa and J-M Maillard and Barry M McCoy}, journal={arXiv: Mathematical Physics}, year={2020} }

We present Painlev{e} VI sigma form equations for the general Ising low and high temperature two-point correlation functions $ C(M,N)$ with $M \leq N $ in the special case $\nu = -k$ where $\nu = \, \sinh 2E_h/k_BT/\sinh 2E_v/k_BT$. More specifically four different non-linear ODEs depending explicitly on the two integers $M $ and $N$ emerge: these four non-linear ODEs correspond to distinguish respectively low and high temperature, together with $ M+N$ even or odd. These four different non…

## References

SHOWING 1-10 OF 19 REFERENCES

Crystal statistics. I. A two-dimensional model with an order-disorder transition

- Materials Science
- 1944

The partition function of a two-dimensional "ferromagnetic" with scalar "spins" (Ising model) is computed rigorously for the case of vanishing field. The eigenwert problem involved in the…

Off-axis correlation functions in the isotropic d=2 Ising model.

- Mathematics, Materials SciencePhysical review. B, Condensed matter
- 1985

A general structural formula is inferred for arbitrary 〈${\ensuremath{\sigma}}_{0}$,0${\mathrm{m}}$,n〉 in terms of complete elliptic integrals K and E.

Holonomy of the Ising model form factors

- Mathematics
- 2006

We study the Ising model two-point diagonal correlation function C(N, N) by presenting an exponential and form factor expansion in an integral representation which differs from the known expansion of…

Introduction to Random Matrices

- Mathematics
- 1993

Here I = S j (a2j 1,a2j) andI(y) is the characteristic function of the set I. In the Gaussian Unitary Ensemble (GUE) the probability that no eigenvalues lie in I is equal to �(a). Also �(a) is a…

Application of the τ-function theory of Painlevé equations to random matrices: PVI , the JUE, CyUE, cJUE and scaled limits

- MathematicsNagoya Mathematical Journal
- 2004

Abstract Okamoto has obtained a sequence of τ-functions for the PVI system expressed as a double Wronskian determinant based on a solution of the Gauss hypergeometric equation. Starting with integral…

Chazy's second-degree Painlevé equations

- Mathematics
- 2006

We examine two sets of second-degree Painlev? equations derived by Chazy in 1909, denoted by systems (II) and (III). The last member of each set is a second-degree version of the Painlev?-VI…

How instanton combinatorics solves Painlevé VI, V and IIIs

- Mathematics
- 2013

We elaborate on a recently conjectured relation of Painlevé transcendents and 2D conformal field theory. General solutions of Painlevé VI, V and III are expressed in terms of c = 1 conformal blocks…

Non-linear partial difference equations for the two-spin correlation function of the two-dimensional Ising model

- Physics, Mathematics
- 1980

Nonlinear Partial Difference Equations for the Two-dimensional Ising Model

- Physics
- 1980

The two-point function of the two-dimensional Ising model at arbitrary temperature is expressed in terms of the solution of a nonlinear partial difference equation. From this difference equation the…

Form factor expansion of the row and diagonal correlation functions of the two-dimensional Ising model

- Physics
- 2006

We derive and prove exponential and form factor expansions of the row correlation function ⟨σ0,0 σ0,N⟩ and the diagonal correlation function ⟨σ0,0 σN,N⟩ of the two-dimensional Ising model.