An inversion-relaxation approach for sampling stationary points of spin model Hamiltonians.
Sampling the stationary points of a complicated potential energy landscape is a challenging problem. Here, we introduce a sampling method based on relaxation from stationary points of the highest index of the Hessian matrix. We illustrate how this approach can find all the stationary points for potentials or Hamiltonians bounded from above, which includes a large class of important spin models, and we show that it is far more efficient than previous methods. For potentials unbounded from above, the relaxation part of the method is still efficient in finding minima and transition states, which are usually the primary focus of attention for atomistic systems.
The Department of Applied Mathematics and Theoretical Physics, The University of Cambridge, Clarkson Road, Cambridge CB3 0EH, United Kingdom.
Ciaran
C
Hughes
Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695, USA.
Dhagash
D
Mehta
Department of Chemistry, The University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.
David J
DJ
Wales