Sherrington-Kirkpatrick Spin Glass

Replica-Symmetric Solution · Order Parameter q · de Almeida-Thouless Instability

Parameters

H = −ΣᵢⱼJᵢⱼsᵢsⱼ − hΣsᵢ
Jᵢⱼ ~ N(J₀/N, J²/N)
RS: q = ∫Dz tanh²(z√q+h)/T
SK model (1975): fully connected Ising model with Gaussian random couplings. Order parameter q = Edwards-Anderson parameter = mean squared magnetization. AT line: replica symmetry broken below T_AT(h,J).
T: 1.0 | q_EA: — | E: — | phase: —