  We use the Jansson-Farrar JF12 magnetic field configuration in the context of
point source searches by correlating the Telescope Array ultra-high energy
cosmic ray data and the IceCube-40 neutrino candidates. As expected, we have
found no correlations, thus, we devote this paper to the study of the effect of
different magnetic field hypotheses on the minimum neutrino source flux
strength required for a $5\sigma$ discovery and the derived $90\%$ CL upper
limits. In this study we present a comparison between the JF12 field, that
includes a combination of regular and random field components, and the standard
turbulent magnetic field used in previous correlation analyses. For a wider
perspective, we also incorporate in our comparison the cases of no magnetic
field and the JF12 regular component alone and consider different power law
indices $\alpha=2,\alpha=2.3$ for the neutrino point source flux. Collaterally,
a novel parameterisation of the JF12 random component is introduced. We have
observed that the discovery potential for a point source search is sensitive to
changes in the magnetic field assumptions, being the difference between the
models mentioned before between 15% and 26%.
