 03200 F. Manzo, F.R. Nardi, E. Olivieri, E. Scoppola
 The easy way to metastability:
tunnelling time and critical configurations
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Apr 29, 03

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Abstract. We consider Metropolis Markov chains with finite state space and
transition probabilities of the form
$$
P(\eta,\eta') = q(\eta,\eta') e^{\beta [H(\eta')  H(\eta)]_+}
$$
for given energy function $H$ and symmetric Markov kernel $q$. We
propose a simple approach to determine the asymptotic behavior,
for large $\beta$, of the first hitting time to the ground state
starting from a particular class of local minima for $H$ called
metastable states.
We separate the asymptotic behavior of the
transition time from the determination of the tube of typical
paths realizing the transition.
This approach turns out to be
useful when the determination of the tube of typical paths is too
difficult, as for instance in the case of conservative dynamics.
We analyze the structure of the saddles introducing the notion of
``essentiality" and describing essential saddles in terms of
``gates". As an example we discuss the case of the 2D Ising Model
in the degenerate case of integer $2J\over h$.
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