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One-Dimensional Impenetrable Anyons in Thermal Equilibrium. III. Large distance asymptotics of the space correlations

Using the determinant representation for the field-field correlation functions of impenetrable anyons at finite temperature obtained in a previous paper, we derive a system of nonlinear partial differential equations completely characterizing the correlators. The system is the same as the one for impenetrable bosons but with different initial conditions. The large-distance asymptotic behavior of the correlation functions is obtained from the analysis of the Riemann-Hilbert problem associated with the system of differential equations. We calculate both the exponential and pre-exponential factors in the asymptotics of the field-field correlators. The asymptotics derived in this way agree with those of the free fermions and impenetrable bosons in the appropriate limits, $κ\to 1$ and $κ\to 0$, of the statistics parameter $κ$, and coincide with the predictions of the conformal field theory at low temperatures.