Simple frustrated systems: chains, strips and squares

The ground-state properties of several systems showing the Toulouse frustration effect are investigated analytically. First, the energy and entropy of the random-bond Ising chain in a uniform field are obtained for all concentrations of antiferromagnetic bonds using the transfer-matrix method. The susceptibility has discontinuities for an infinite number of critical values of the field, where the entropy shows spikes in addition to discontinuities. These effects are related to the physics of frustration. The second system studied consists of frustrated strips, which it is argued are the proper one-dimensional limit of spin glasses. Two kinds of strips are considered and the results are compared with recent numerical works on two-dimensional spin glasses and with the exact results for random (3*3) squares.