  Using quasi-exact numerical density-matrix renormalization-group techniques
we calculate the critical Casimir force for a two-dimensional (2D) Ising strip
with equal strong surface fields, along the thermodynamic paths corresponding
to the fixed nonzero bulk field h<>0. Using the Derjaguin approximation we also
determine the critical Casimir force and its potential for two discs. We find
that varying the temperature along the iso-fields lying between the bulk
coexistence and the capillary condensation critical point leads to a dramatic
increase of the critical Casimir interactions with a qualitatively different
functional dependence on the temperature than along h=0. These findings might
be of relevance for biomembranes, whose heterogeneity is recently interpreted
as being connected with a critical behavior belonging to the 2D Ising
universality class.
