The emptiness formation probability of the XY chain, in the double-scaling limit near its critical lines, is governed by a Painleve V tau function; the result is exact at the Ising point and numerically supported elsewhere.
From Form Factors to Correlation Functions: The Ising Model
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abstract
Using exact expressions for the Ising form factors, we give a new very simple proof that the spin-spin and disorder-disorder correlation functions are governed by the Painlev\'e III non linear differential equation. We also show that the generating function of the correlation functions of the descendents of the spin and disorder operators is a $N$-soliton, $N\to\infty$, $\tau$-function of the sinh-Gordon hierarchy. We discuss a relation of our approach to isomonodromy deformation problems, as well as further possible generalizations.
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Emptiness formation probability and Painlev\'e V equation in the XY spin chain
The emptiness formation probability of the XY chain, in the double-scaling limit near its critical lines, is governed by a Painleve V tau function; the result is exact at the Ising point and numerically supported elsewhere.