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framework:topological-constraints-on-self-organisation-framework

Topological constraints on self-organisation framework

Main framework: uses scaling of free energy under domain wall formation to determine whether local interactions can sustain ordered phases based on graph topology alone

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Thinkers (3)

thinker

Methods (2)

method
  • Peierls argument
    cites
    Classical proof technique for existence of phase transitions in dimensions >1 via domain wall perimeter scaling; adapted in Theorem 1
  • Landau–Lifshitz scaling argument
    cites
    Historical technique for proving absence of phase transitions via free energy scaling; generalized in this paper to arbitrary local Hamiltonians

Frameworks (5)

framework
  • Topological constraints on self-organization
    related_to
    Core framework: necessary conditions on graph topology for ordered phases to exist in locally-interacting systems.
  • transformer architecture
    cites
    Neural network architecture based on attention, commonly used in large language models
  • Autoregressive models
    cites
    Second model system studied; used to show why flat autoregressive LLMs struggle with long-range coherence.
  • Potts model
    cites
    One of three model systems studied to analyze free-energy scaling and domain-wall formation in self-organizing systems.
  • Windowed Hamiltonian
    implements
    Core technical concept: a Hamiltonian where spin-spin interactions are defined only within finite windows ω, enabling generic analysis across diverse lattices

Related by similarity (8)

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