Computational Science Technical Note CSTN-205

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Optimising Computations for Evaluating Ising and Potts Model Partition Functions by Exact Enumeration

K. A. Hawick and D. P. Playne

Archived: 2013

Abstract

The Ising and Potts discrete lattice are useful baselines of comparison for many systems and theoretical calculations in statistical physics. While these models are traditionally studied using Monte Carlo sampling techniques it is also useful to exactly enumerate their partition functions using brute-force coding techniques. Recent advances in bitwise manipulation and parallel processing technology have made these techniques computationally feasible for the Q=3,4 state Potts model as well as the 2 state Ising spin model. We report on bit-packing and graphical processing unit implementations to improve the number of model states that can be exactly enumerated per second and discuss implications for uses of this approach with various observables.

Keywords: partition function; enumeration; brute force; summation; multicore, GPU

Full Document Text: PDF version.

Citation Information: BiBTeX database for CSTN Notes.

BiBTeX reference:

@INPROCEEDINGS{CSTN-205,
        author = {K. A. Hawick and D. P. Playne},
        title = {Optimising Computations for Evaluating Ising and Potts Model Partition
                Functions by Exact Enumeration},
        booktitle = {Proc. 9th International Conference on Foundations of Computer Science
                (FCS'13)},
        year = {2013},
        number = {CSTN-205},
        pages = {FCS4072},
        address = {Las Vegas, USA},
        month = {22-15 July},
        publisher = {WorldComp},
        institution = {Computer Science, Massey University,m Auckland, New Zealand},
        keywords = {partition function; enumeration; brute force; summation; multicore,
                GPU},
        owner = {kahawick},
        timestamp = {2013.04.22}
}


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