"Exact" Algorithm for Random-Bond Ising Models in 2D

Details "Exact" Algorithm for Random-Bond Ising Models in 2D "Exact" Algorithm for Random-Bond Ising Models in 2D

2006-10-30

arxiv.org/abs/cond-mat/0610822v1

Physics

Condensed Matter

Statistical Mechanics

4.2 pages, 5 figures, accepted for publication in Phys. Rev. Lett

Scientific paper

10.1103/PhysRevLett.97.227205

We present an efficient algorithm for calculating the properties of Ising models in two dimensions, directly in the spin basis, without the need for mapping to fermion or dimer models. The algorithm gives numerically exact results for the partition function and correlation functions at a single temperature on any planar network of N Ising spins in O(N^{3/2}) time or less. The method can handle continuous or discrete bond disorder and is especially efficient in the case of bond or site dilution, where it executes in O(L^2 ln L) time near the percolation threshold. We demonstrate its feasibility on the ferromagnetic Ising model and the +/- J random-bond Ising model (RBIM) and discuss the regime of applicability in cases of full frustration such as the Ising antiferromagnet on a triangular lattice.

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