  The confinement of long-ranged critical fluctuations in the vicinity of
second-order phase transitions in fluids generates critical Casimir forces
acting on confining surfaces or among particles immersed in a critical solvent.
This is realized in binary liquid mixtures close to their consolute point
$T_{c}$ which belong to the universality class of the Ising model. The
deviation of the difference of the chemical potentials of the two species of
the mixture from its value at criticality corresponds to the bulk magnetic
filed of the Ising model. By using Monte Carlo simulations for this latter
representative of the corresponding universality class we compute the critical
Casimir force as a function of the bulk ordering field at the critical
temperature $T=T_{c}$. We use a coupling parameter scheme for the computation
of the underlying free energy differences and an energy-magnetization
integration method for computing the bulk free energy density which is a
necessary ingredient. By taking into account finite-size corrections, for
various types of boundary conditions we determine the universal Casimir force
scaling function as a function of the scaling variable associated with the bulk
field. Our numerical data are compared with analytic results obtained from
mean-field theory.
