Approximability of the Ground State Problem for Certain Ising Spin Glasses

Alberto Bertoni, Paola Campadelli, Cristina Gangai, Roberto Posenato
1997 Journal of Complexity  
We consider polynomial time algorithms for finding approximate solutions to the ground state problem for the following three-dimensional case of an Ising spin glass: 2n spins are arranged on a two-level grid with at most n γ vertical interactions (0 ≤ γ ≤ 1). The main results are: 1. Let 1 2 ≤ γ < 1. There is an approximate polynomial time algorithm with absolute error less than n γ for all n; there exists a constant β > 0 such that every approximate polynomial time algorithm has absolute error
more » ... greater than βn γ infinitely often, unless P = NP. 2. Let γ = 1. There is an approximate polynomial time algorithm with absolute error less than n/lg n; there exists a number k > 1 such that every approximate polynomial time algorithm has absolute error greater than n/(lg n) k infinitely often iff NP ⊆ ε>0 DTIME(2 n ε ).
doi:10.1006/jcom.1997.0449 fatcat:ghrd2c2ufzbufpkicsfwzaymle