Lattice topology and thermodynamic phase transitions

How combinatorial structure of local Hamiltonians determines free energy equivalence classes and long-range order feasibility across temperature regimes.

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The papers/notes whose extracted claims & findings make up this cluster.

Topological constraints on self-organisation in locally interacting systems3 members

Bridges (4)

Other communities that share members with this one — cross-cutting threads or papers that sit at the seam between two themes.

Causal emergence in biological systems3 shared
Hierarchical structure and multiscale coherence in physical systems3 shared
Hierarchical network ordering & thermodynamics2 shared
Lattice Hamiltonian free energy universality1 shared

Findings (2)

All local Hamiltonians on lattices with the same combinatorial structure have asymptotically equivalent free energies (Theorem 1)Topological equivalence theorem for local Hamiltonians
For one-dimensional local Hamiltonian with m>1 stored patterns at non-zero temperature, domain wall formation is thermodynamically favourable (Theorem 2)No ordered phase in 1D with multiple stored patterns

Claims (1)

Topology is the critical factor differentiating systems capable of long-range order from those that are not.Key interpretive position: topological properties of interaction graphs determine whether systems can self-organize, independent of substrate