The first result is a refinement of the celebrated theorem independently established by Aizenman and Higuchi in the late 1970s, which states that all infinite volume Gibbs measures of the ferromagnetic nearest-neighbor Ising model on Z^2 are of the form О±P+ +(1в€’О±)Pв€’, О±в€€, where P+ and Pв€’ are the two pure phases of the model. The analysis of interfaces fluctuations plays a crucial role in this domain. In the first part of the thesis, we study the set of infinite volume Gibbs measures of the Ising and Potts models in the phase coexistence regime, i.e.

It is organized in two parts dealing with quite different problematics. liquid-vapor, positive-negative magnetization). they constitute a modelization of interfaces between several phases (e.g. This thesis is devoted to several models of Statistical Mechanics which can be seen as interfaces models, i.e. Transitions in statistical mechanical models. On a possible application of pre-injective factor maps in the study of phase Gibbs measure under a pre-injective factor map is not a Gibbs measure. We provide a sufficient condition under which the image of a Under a pre-injective factor map between shifts of finite type is always a Others), and pose several open questions.ДЄs an aside, it turns out that a shift-invariant pre-image of a Gibbs measure The randomization property of algebraic cellular automata (as suggested by Reversible cellular automata is missing, but we speculate on the relevance of A general description of approach to equilibrium in Transpose cannot preserve any full-support Markov measure other than the One-dimensional reversible cellular automaton that has a positively expansive Measures other than the uniform Bernoulli measure. We obtain that strongly transitive cellular automata have no invariant Gibbs Known to be invariant under every surjective cellular automaton, and whichД¬orresponds to the conservation of the trivial Hamiltonian.

A special case is the uniform Bernoulli measure, which is well Surjective cellular automaton if and only if the cellular automaton conserves Shift-invariant Gibbs measures associated to a Hamiltonian is invariant under a Thermodynamic equilibrium) and the conservation of additive quantities in The invariance of Gibbs measures (used in statistical mechanics to describe Nevertheless, we establish a connection between Characterizing all the invariant measures of a cellularДЄutomaton could be challenging. Their states of macroscopic equilibrium are described using invariant Reversible cellular automata are seen as microscopic physical models, and

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