Statistical Topography of Random Energy Surfaces in a Spin Glass Cluster

Hierarchical random energy model of a spin glass.

We introduce a random energy model on a hierarchical lattice where the interaction strength between variables is a decreasing function of their mutual hierarchical distance, making it a non-mean-field model. Through small coupling series expansion and a direct numerical solution of the model, we provide evidence for a spin-glass condensation transition similar to the one occurring in the usual ...

Twist Free Energy in a Spin Glass

The field theory of a short range spin glass with Gaussian random interactions, is considered near the upper critical dimension six. In the glassy phase, replica symmetry breaking is accompanied with massless Goldstone modes, generated by the breaking of reparametrization invariance of a Parisi type solution. Twisted boundary conditions are thus imposed at two opposite ends of the system in ord...

Cluster–Exact Approximation of Spin Glass Groundstates

We present an algorithm which calculates groundstates of Ising spin glasses approximately. It works by randomly selecting clusters of spins which exhibit no frustrations. The spins which were not selected, contribute to the local fields of the selected spins. For the spin–cluster a groundstate is exactly calaculated by using graphtheoretical methods. The other spins remain unchanged. This proce...

Statistical Properties of Random Spin

Spin-Glass and Related Orderings in Quenched Random-Spin Systems

A general model in which the nearest-neighbor exchange interactions J(x⃗ ,x⃗ ′) are of the form J(x⃗ ,x⃗ ′)=J1+J2ε(x⃗ )ε(x⃗ ′)+J3[ε(x⃗ )+ε(x⃗ ′)]+J4μ(x⃗ ,x⃗ ′) is considered. Here ε(x⃗ ) is a random site variable and μ(x⃗ ,x⃗ ′) is a random bond variable. It is argued that J4 tends to produce the Edwards-Anderson-type spin glass, whereas J2 produces a different type of phase which is like an alloy of up and...