3 problems

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Conjecture on nonempty Gibbs measures for the planar polygonal field
Gibbs-measure existence conjecture. The family
Conjectureopengibbs-measures polygonal-markov-fields thermodynamic-limitsarXiv posted 2 days ago
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Conjecture on untempered thermodynamic limits for polygonal Markov fields at zero temperature
Untempered-limit conjecture. Untempered thermodynamic limits should exist even for
Conjectureopenpolygonal-markov-fields thermodynamic-limitsarXiv posted 2 days ago
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Conjecture on symmetry-breaking infinite-volume phases for polygonal Markov fields
Symmetry-breaking phase conjecture. For $\alpha=0$ , outside the class of measures without infinite contours, there exists an infinite number of extreme infinite-volume phases break…
Conjectureopenpolygonal-markov-fields symmetry-breaking thermodynamic-limitsarXiv posted 2 days ago

Conjecture on nonempty Gibbs measures for the planar polygonal field