2 Computing Exact Ground Statesof Hard Ising Spin Glass Problemsby Branch-and-Cut

Whenstudyinggroundstatepropertiesof Isingspinglasses, thecomputationof exactground states,i.e., spincon gurations with exact ratherthanapproximateminimumenergy, is often desirable. The Ising model is oneof the mostcommonlyused,both for its simplicity and its accuracy in describingmany realworld systems.Whenwe refer to a “spinglass” in this chapter , wealwayshavetheIsingmodelin mind. The con gurations that are mostly consideredin the literatureare the twoand threedimensional Isingspinglassesonagrid with nearest neighborinteractionsandfreeor periodic boundaryinteractions,with or without an exterior magnetic eld.The periodic boundary conditionsare a standardway of approximatingan in nitespin glasswith a structurethat containsonly a nitenumberof spins. Unfortunately, therearenofunctionsin closedform that,givenall interactionsbetweenthe spinsandtheexterior eld, yield agroundstate.Therefore,theonly wayto computeaground