  We solve a two dimensional model for polymer chain folding in the presence of
mechanical pulling force ($f$) exactly using equilibrium statistical mechanics.
Using analytically derived expression for the partition function we determine
the phase diagram for the model in the $f$-temperature ($T$) plane. A square
root singularity in the susceptibility indicates a second order phase
transition from a folded to an unfolded state at a critical force ($f_c$) in
the thermodynamic limit of infinitely long polymer chain. Surprisingly, the
temperature dependence of $f_c$ shows a reentrant phase transition, which is
reflected in an increase in $f_c$ as $T$ increases below a threshold value. For
a range of $f$ values, the unfolded state is stable at both low and high
temperatures. The high temperature unfolded state is stabilized by entropy
whereas the low temperature unfolded state is dominated by favorable energy.
The exact calculation could serve as a bench mark for testing approximate
theories that are used in analyzing single molecule pulling experiments.
