Ising field theory in a magnetic field: Analytic properties of the free energy

We study the analytic properties of the scaling function associated with the 2D Ising model free energy in the critical domain T --> T-c, H --> 0. The analysis is based on numerical data obtained through the Truncated Free Fermion Space Approach. We determine the discontinuities across the Yang Lee and Langer branch cuts. We confirm the standard analyticity assumptions and propose extended analyticity; roughly speaking, the latter states that the Yang Lee branching point is the nearest singularity under Langer s branch cut. We support the extended analyticity by evaluating numerically the associated extended dispersion relation.