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This work presents the derivation of the large time and distance asymptoticbehavior of the field-field correlation functions of impenetrableone-dimensional anyons at finite temperature. In the appropriate limits of thestatistics parameter, we recover the well-known results for impenetrable bosonsand free fermions. In the low-temperature (usually expected to be the"conformal") limit, and for all values of the statistics parameter away fromthe bosonic point, the leading term in the correlator does not agree with theprediction of the conformal field theory, and is determined by the singularityof the density of the single-particle states at the bottom of thesingle-particle energy spectrum.

One-Dimensional Impenetrable Anyons in Thermal Equilibrium. IV. Large Time and Distance Asymptotic Behavior of the Correlation Functions