Accession Number : ADA256580


Title :   Implementation of Minimal Representations in 2d Ising Model Calculations


Corporate Author : CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS


Personal Author(s) : Parlett, Beresford ; Heng, Wee-Liang


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/a256580.pdf


Report Date : May 1992


Pagination or Media Count : 64


Abstract : We present a new method for approximating the partition function of 2D Ising models using a transfer matrix of order 2n. For n = 30 our current program took about 20 seconds on a Sparc station to obtain 4 correct decimals in the top two eigenvalues and 5 minutes for 6 correct decimals. Eigenvectors were computed at the same time. The temperature was within 3% of critical. The main idea. is to force certain entries in vectors to have the same values and to find the crudest representation of this type that delivers the required accuracy. At no time does our program work with vectors with 2n entries.


Descriptors :   *ALGORITHMS , *MATRICES(MATHEMATICS) , FUNCTIONS , STATIONS , ACCURACY , TIME , VALUE , TRANSFER , WORK , EIGENVALUES , EIGENVECTORS , TEMPERATURE , MODELS


Subject Categories : Numerical Mathematics


Distribution Statement : APPROVED FOR PUBLIC RELEASE