  We study the lifetime of locally stable states in the Thirring model, which
describes a system of particles whose interactions are long-range. The model
exhibits first-order phase transitions in the canonical ensemble and,
therefore, a free energy barrier separates two free energy minima. The energy
of the system diffuses as a result of thermal fluctuations and we show that its
dynamics can be described by means of a Fokker-Planck equation. Considering an
initial state where the energy takes the value corresponding to one of the
minima of the free energy, we can define the lifetime of the initial state as
the mean first-passage time for the system to reach the top of the free energy
barrier between the minima. We use an analytical formula for the mean
first-passage time which is based on the knowledge of the exact free energy of
the model, even at a finite number of particles. This formula shows that the
lifetime of locally stable states increases exponentially in the number of
particles, which is a typical feature of systems with long-range interactions.
We also perform Monte Carlo simulations in the canonical ensemble in order to
obtain the probability distribution of the first-passage time, which turns out
to be exponential in time in a long time limit. The numerically obtained mean
first-passage time agrees with the theoretical prediction. Combining theory and
simulations, our work provides a new insight in the study of metastability in
many-body systems with long-range interactions.
