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This volume is a synopsis of recent works aiming at a mathematically rigorous justification of the phase coexistence phenomenon, starting from a microscopic model. It is intended to be self-contained. Those proofs that can be found only in research papers have been included, whereas results for which the proofs can be found in classical textbooks are only quoted.

Ising-model. --- Percolatietheorie. --- Phase transformations (Statistical physics) --- Ising model. --- Percolation (Statistical physics) --- Transformations de phase (Physique statistique) --- Ising model --- Percolation (Physique statistique) --- Electronic books. -- local. --- Ising model -- Congresses. --- Percolation (Statistical physics) -- Congresses. --- Phase transformations (Statistical physics) -- Congresses. --- Wulff construction (Statistical physics) -- Congresses. --- Atomic Physics --- Mathematical Statistics --- Mathematics --- Physics --- Physical Sciences & Mathematics --- Wulff construction (Statistical physics) --- Lenz-Ising model --- Mathematics. --- Calculus of variations. --- Probabilities. --- Physics. --- Probability Theory and Stochastic Processes. --- Theoretical, Mathematical and Computational Physics. --- Calculus of Variations and Optimal Control; Optimization. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Math --- Science --- Lattice theory --- Statistical physics --- Ferromagnetism --- Distribution (Probability theory. --- Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Operations research --- Simulation methods --- System analysis --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Mathematical physics. --- Physical mathematics --- Phase changes (Statistical physics) --- Phase transitions (Statistical physics) --- Phase rule and equilibrium