Trivial Ground State Structure in the Two-Dimensional Ising Spin Glass

TL;DR

This paper investigates the ground state structure of the 2D Ising spin glass with Gaussian interactions, showing that only a single pure state exists at zero temperature, consistent with the droplet model.

Contribution

It provides evidence that the 2D Ising spin glass has a trivial ground state structure with a single pure state, supported by boundary condition analysis and fractal dimension estimates.

Findings

Probability of spin orientation change decreases as L^{-0.70}

Fractal dimension of domain walls is consistent with previous estimates

Supports the droplet model prediction of a single pure state

Abstract

We study how the ground state of the two-dimensional Ising spin glass with Gaussian interactions in zero magnetic field changes on altering the boundary conditions. The probability that relative spin orientations change in a region far from the boundary goes to zero with the (linear) size of the system L like L^{-lambda}, where lambda = -0.70 +/- 0.08. We argue that lambda is equal to d-d_f where d (=2) is the dimension of the system and d_f is the fractal dimension of a domain wall induced by changes in the boundary conditions. Our value for d_f is consistent with earlier estimates. These results show that, at zero temperature, there is only a single pure state (plus the state with all spins flipped) in agreement with the predictions of the droplet model.