Transverse Ising Spin Glass and Random Field Systems

Abstract

Transverse Ising systems with randomly frustrated interactions or random fields have an intriguing nature that a phase transition peculiar in randomly frustrated systems is driven by tunable thermal fluctuations as well as quantum fluctuations. The first part of Chap. 6 discusses transverse Ising spin glasses in great detail, where systems are characterised by randomly competing interactions and a uniform transverse field. It includes analytic and numerical studies of the Sherrington-Kirkpatrick model in a transverse field, numerical studies of the Edwards-Anderson model in a transverse field in two and three dimensions, and the mean field theory of Ising spin glasses with random p-body interactions in a transverse field. One of the interesting problem in quantum spin glasses is the stability of the state with replica symmetry breaking in quantum fluctuations. This problem is also mentioned. The second part of Chap. 6 focuses on the random field transverse Ising models. Phase diagrams at zero and finite temperatures are studied by the mean field theory. Appendices of this chapter include a brief note on the infinite-range vector (Heisenberg) spin glass model, mapping of the transverse Ising spin glass Hamiltonian to an effective classical Hamiltonian, mapping of random field Ising ferromagnet in a transverse field to a random Ising antiferromagnet in a longitudinal and transverse fields, and mathematical details of the replica method in transverse Ising spin glasses.