Solving the Ising model exactly on a 5×5×4 lattice using the Connection machine

Gyan Bhanot, Srikanth Sastry

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


We implement a recently proposed exact method for solving distrete statistical models for the 3-dimensional Ising model with open boundary conditions. Our computations were done on the Connection machine because the problem maps very naturally onto massively parallel architectures. We explicitly calculate the number of states of the system at each energy for systems of size 5×4×Lz, for Lz≤5. On serial or vector computers, the time for the computation scales with the volume V like V2LλLy. On the Connection Machine, the calculation can be spread across the processors. This decreases the computation requirements by a factor equal to the number of processors. We describe the method, its implementation on the Connection Machine both in PARIS and in FORTRAN, and our results. We also state the requirements for solving larger systems using this method.

Original languageEnglish (US)
Pages (from-to)333-346
Number of pages14
JournalJournal of Statistical Physics
Issue number3-4
StatePublished - Aug 1990
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


  • Ising
  • critical exponents
  • exact
  • massively-parallel architecture
  • partition function
  • zeros


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