Spin Glass Primer
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Spin Glass Primer

Encyclopedia of Complexity at Criticality

Core Phenomena

Phase Transitions

Tc = Critical threshold where:
⟨σiσj⟩ ∼ Jij/rη + ⋯

Applications: Neural networks freezing • Social consensus formation • Protein folding energy landscapes

Methodological Toolkit

Renormalization Group Flow

"The essence of critical phenomena is the existence of fluctuations at all length scales" — Wilson (1982)

Implementation Steps

      Coarse-grain system (k → Λ/b)
      Rescale variables (x → x/b)
      Find fixed points (β(g*) = 0)

Network Science Synthesis

Ising model meets Barabási-Albert:
⟨k⟩ = ∫ P(k) dk → ⟨k²⟩ diverges at critical pc

Current research: Community detection via replica method • Cryptoeconomic phase diagrams

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