Implementation of Minimal Representations in 2d Ising Model Calculations

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.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
May 01, 1992
Accession Number
ADA256580

Entities

People

  • Beresford Parlett
  • Wee-liang Heng

Organizations

  • University of California, Berkeley

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Applied Mathematics
  • Computations
  • Computer Science
  • Computers
  • Critical Temperature
  • Eigenvalues
  • Eigenvectors
  • Floating Point Operations
  • Identities
  • Magnetic Fields
  • Mathematics
  • Matrix Theory
  • Notation
  • Numbers
  • Theorems
  • Two Dimensional

Readers

  • Database Systems and Applications
  • Linear Algebra
  • Regression Analysis.