Sergio Caracciolo, Alexander K. Hartmann, Scott Kirkpatrick, Martin Weigel
Published 2023-01-02Version 1
The chapter starts with a historical summary of first attempts to optimize the spin glass Hamiltonian, comparing it to recent results on searching largest cliques in random graphs. Exact algorithms to find ground states in generic spin glass models are then explored in Section 1.2, while Section 1.3 is dedicated to the bidimensional case where polynomial algorithms exist and allow for the study of much larger systems. Finally Section 1.4 presents a summary of results for the assignment problem where the finite size corrections for the ground state can be studied in great detail.
Comments: 24 pages, 4 figures, to appear as a contribution to the edited volume "Spin Glass Theory & Far Beyond - Replica Symmetry Breaking after 40 Years", World Scientific
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