Implementation of Minimal Representations in 2d Ising Model Calculations
CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS
Pagination or Media Count:
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.
- Numerical Mathematics