ON THE GROUND-STATE PROPERTIES OF THE +/- J ISING-MODEL

H Ulman, M Athematics J Ournal

Bernd A. Berg, Ulrich H. E. Hansmann, Thomas Neuhaus

之康 尾関, Yukiyasu Ozeki

John A. Blackman, J. Poulter

In the combinatorial method or Grassmann algebra formalism the ground state properties of the f J Ising \nmodel can be expressed in terms of the behaviour of the eigenvectors of a matrix. It is shown that a transition from \nlocalized to extended eigenvectors signals the breakdown of ferromagnetic rigidity.

之康 尾関, Yukiyasu Ozeki

Shu Tanaka

In this paper we show quantum fluctuation effect of fully frustrated Ising spin systems. Quantum annealing has been expected to be an efficient method to find ground state of optimization problems. However it is not clear when to use the quantum annealing. In order to clarify when the quantum annealing works well, we have to study microscopic properties of quantum annealing. In fully frustrated Ising spin systems, there are macroscopically degenerated ground states. When we apply quantum annealing to fully frustrated systems, we cannot obtain each ground state with the same probability. This nature is consistent with "order by disorder" which is well-known mechanism in frustrated systems.