  Trust is a collective, self-fulfilling phenomenon that suggests analogies
with phase transitions. We introduce a stylized model for the build-up and
collapse of trust in networks, which generically displays a first order
transition. The basic assumption of our model is that whereas trust begets
trust, panic also begets panic, in the sense that a small decrease in trust may
be amplified and ultimately lead to a sudden and catastrophic drop of trust. We
show, using both numerical simulations and mean-field analytic arguments, that
there are extended regions of the parameter space where two equilibrium states
coexist: a well-connected network where confidence is high, and a poorly
connected network where confidence is low. In these coexistence regions,
spontaneous jumps from the well-connected state to the poorly connected state
can occur, corresponding to a sudden collapse of trust that is not caused by
any major external catastrophe. In large systems, spontaneous crises are
replaced by history dependence: whether the system is found in one state or in
the other essentially depends on initial conditions. Finally, we document a new
phase, in which agents are connected yet distrustful.
