The phase transition phenomena in the Ising model are widely investigated. The authors discuss the probabilistic interpretation of the droplet condensation. It appears that the droplet condensation can be indeed observed in the low temperature Ising model, where the role of two substances is played by the two different phases. The condensation takes place when the amount of the solvent exceeds the threshold which is equal to the volume of the system raised to a certain power smaller than one. From the probability theory point of view it follows that the threshold belongs to the so-called region of moderate deviations. Phenomenon of condensation is a question about the behavior of the probabilities of large and moderate deviations in the phase transition regime. It turns out that the condensation regime is precisely the regime where this behavior is different from the one given by the classical schemes of the probability theory of independent or weakly dependent random variables. An overview of results of the classical probability theory on large and moderate deviations is given and compared with the corresponding results for the Ising model. The description of the Ising model is given as well. The complete results have been appeared [in: Probability contributions to statistical mechanics. Adv. Sov. Math. 20, 91-219 (1994; Zbl 0815.60024)].
For the entire collection see [Zbl 0818.00015].