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Quenched and annealed critical points in polymer pinning models. (English) Zbl 1188.82154

A polymer pinning model is mathematically defined by a Markov chain on a state space which comprises a special point \(0\) where the polymer interacts with a potential. The physical configuration of the polymer is pictured by the space-time trajectory of the Markov chain. The problem of interest here is to examine how the presence of a random potential does affect the path properties of the Markov chain, and how to distinguish the disordering case from the homogeneous one; and it can be tackled by means of the quenched contact function. The effect of disorder is studied by comparing the quenched pinning model to its annealed counterpart, which is obtained via an averaging of the Gibbs weight over the disorder. It is shown that under some given conditions for the system parameters, they are identical whilst under some others they are different.

MSC:

82D60 Statistical mechanics of polymers
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
82B26 Phase transitions (general) in equilibrium statistical mechanics
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References:

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