| Autor: |
Boukraa, S, Maillard, J-M, McCoy, B M |
| Předmět: |
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| Zdroj: |
Journal of Physics A: Mathematical & Theoretical; Nov2020, Vol. 53 Issue 46, p1-34, 34p |
| Abstrakt: |
We present Painlevé VI sigma form equations for the general Ising low and high temperature two-point correlation functions C(M, N) with M ⩽ N in the special case ν = −k where ν = sinh 2Eh/kBT/sinh 2Ev/kBT. 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-linear ODEs are also valid for M ⩾ N when ν = −1/k. For the low-temperature row correlation functions C(0, N) with N odd, we exhibit again for this selected ν = −k condition, a remarkable phenomenon of a Painlevé VI sigma function being the sum of four Painlevé VI sigma functions having the same Okamoto parameters. We show in this ν = −k case for T < Tc and also T > Tc, that C(M, N) with M ⩽ N is given as an N × N Toeplitz determinant. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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