The method of minimal representations in 2D Ising model calculations

✍ Scribed by Beresford N. Parlett; Wee-Liang Heng

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 533 KB
• Volume: 114
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1994.1164

✦ Synopsis

We present a new method for approximating the partition function of 2D Ising models using a transfer matrix of order 2". For n=30 our current program took about 20 s on a Sparc station to obtain four correct decimals in the top two eigenvalues and 5 rain for six 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 2" entries.