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

Abstract

We study the analytic properties of the scaling function associated with the 2D Ising model free energy in the critical domain $T\to T_c$, $H\to 0$. 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".

65 pages, 23 eps figures; uses harvmac.tex