PARAMETERS
PHYSICS
Ĥ = i^(q/2) Σ J_{i₁..iᵣ} ψᵢ₁···ψᵢᵩ
The SYK model describes N Majorana fermions with random q-body all-to-all interactions drawn from a Gaussian ensemble ⟨J²⟩ = J²(q-1)!/N^(q-1).
Key features:
· Maximal Lyapunov exponent λ_L = 2π/β (saturates MSS bound)
· Conformal IR: G(τ) ~ |τ|^(-2/q)
· Holographic dual to JT gravity (near-extremal black holes)
· Zero-dimensional, exactly solvable via large-N Schwinger-Dyson
Key features:
· Maximal Lyapunov exponent λ_L = 2π/β (saturates MSS bound)
· Conformal IR: G(τ) ~ |τ|^(-2/q)
· Holographic dual to JT gravity (near-extremal black holes)
· Zero-dimensional, exactly solvable via large-N Schwinger-Dyson