Abstract
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 computes 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(NlnN) time near the percolation threshold. We demonstrate its feasibility on the ferromagnetic Ising model and the +/- J random-bond Ising model and discuss the regime of applicability in cases of full frustration such as the Ising antiferromagnet on a triangular lattice.
Published in:
Physical Review Letters 97,22 (2006) 227205;
Link to original published article:
http://link.aps.org/doi/10.1103/PhysRevLett.97.227205
Keywords
spin-glass;; transition;; order
Date of Version
January 2006
Recommended Citation
Loh, Y. L. and Carlson, E. W., "Efficient algorithm for random-bond ising models in 2D" (2006). Department of Physics and Astronomy Faculty Publications. Paper 276.
https://docs.lib.purdue.edu/physics_articles/276