id: 04011783
dt: j
an: 04011783
au: Batchelor, Murray T.
ti: Sparse matrix factorizations of transfer matrices.
so: J. Aust. Math. Soc., Ser. B 28, 462-475 (1987).
py: 1987
pu: Australian Mathematical Society c/o Australian National University,
    Mathematics Department, Canberra
la: EN
cc: 
ut: sparse matrix factorization; interactions round a face model; leading
    eigenvalues; transfer matrix; Ising model; interacting spins; delta
    functions
ci: 
li: doi:10.1017/S0334270000005531
ab: For easing the computational effort in obtaining the leading eigenvalues a
    factorization of the transfer matrix into a product of sparse matrices
    is used. This paper is reviewing first the factorizations of the
    interactions round a face model in which the first and second neighbour
    interactions are contained. The sparse factors of a more general Ising
    model containing first, second and third neighbour interactions are
    also presented. For each considered case the formulation of the
    transfer matrix as a product of sparse factors is achieved by viewing
    the auxiliary spin sets required as a hierarchy of interacting spins.
    The majority of these spins interact through delta functions, giving
    rise to sparse nature of the factors. Each factor of the transfer
    matrix can be thought of as arising from the fundamental units (faces
    or wedges) in a given row. Using the sparse matrix representation, a
    significant reduction of the work requirement for computing the leading
    eigenvalues of the transfer matrix is achieved.
rv: I.Arany