96 research outputs found
Weak versus strong uniqueness of Gibbs measures: a regular short-range example
No full textWe provide an example of a nearest-neighbour random model on a regular lattice which, almost certainly, has a unique (disordered) Gibbs state for every boundary condition, although by choosing interaction-dependent boundary conditions, one can obtain different Gibbs states.
A Note on the Stability of Phase Diagrams in Lattice Systems
No full textWe construct a class of non-symmetry breaking pair interactions, which change the phase diagram of the n.n. Ising and classical XY model. Furthermore we improve earlier obtained constraints on the decrease of interactions, necessary to get analyticity properties of the pressure in manifolds of non-symmetry breaking interactions.
Spin-Flip Dynamics of the Curie-Weiss Model: Loss of Gibbsianness with Possibly Broken Symmetry
Get PDFWe study the conditional probabilities of the Curie-Weiss Ising model in vanishing external field under a symmetric independent stochastic spin-flip dynamics and discuss their set of points of discontinuity (bad points). We exhibit a complete analysis of the transition between Gibbsian and non-Gibbsian behavior as a function of time, extending the results for the corresponding lattice model, where only partial answers can be obtained. For initial temperature β^−1 ≥ 1, we prove that the time-evolved measure is always Gibbsian. For ⅔ ≤ β^−1 < 1, the time-evolved measure loses its Gibbsian character at a sharp transition time. For β^−1 < ⅔, we observe the new phenomenon of symmetry-breaking in the set of points of discontinuity: Bad points corresponding to non-zero spin-average appear at a sharp transition time and give rise to biased non-Gibbsianness of the time-evolved measure. These bad points become neutral at a later transition time, while the measure stays non-Gibbs. In our proof we give a detailed description of the phase-diagram of a Curie-Weiss random field Ising model with possibly non-symmetric random field distribution based on bifurcation analysis.
Chopper model of pattern recognition
Get PDFA simple model is proposed that allows an efficient storage and retrieval of random patterns. Also correlated patterns can be handled. The data are stored in an Ising-spin system with ferromagnetic interactions between all the spins and the main idea is to "chop" the system along the boundaries where the patterns differ.
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