Model of a quasi-one-dimensional spin glass

We consider a system of linear chains of Ising spins with short-range nearest-neighbor ferromagnetic interactions of strength K along the chains, and with infinite-range random interchain interactions of a Sherrington-Kirkpatrick type. Also included in the model is a local Gaussian random field with variance Δ. In the replica symmetric case, the system is mapped exactly on the one-dimensional Ising model in a random field and a recursion method for calculating the spin-correlation functions is developed. For Δ=0, an analytic relation for freezing temperature ${\mathit{T}}_{\mathit{f}}$(K) is obtained. The replica-symmetric spin-glass phase is shown to be stable above the freezing temperature ${\mathit{T}}_{\mathit{f}}$(K,Δ), which is determined numerically.