Numerically exact correlations and sampling in the two-dimensional Ising spin glass

Creighton K. Thomas, Arthur Alan Middleton

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

A powerful existing technique for evaluating statistical mechanical quantities in two-dimensional Ising models is based on constructing a matrix representing the nearest-neighbor spin couplings and then evaluating the Pfaffian of the matrix. Utilizing this technique and other more recent developments in evaluating elements of inverse matrices and exact sampling, a method and computer code for studying two-dimensional Ising models is developed. The formulation of this method is convenient and fast for computing the partition function and spin correlations. It is also useful for exact sampling, where configurations are directly generated with probability given by the Boltzmann distribution. These methods apply to Ising model samples with arbitrary nearest-neighbor couplings and can also be applied to general dimer models. Example results of computations are described, including comparisons with analytic results for the ferromagnetic Ising model, and timing information is provided.

Original languageEnglish (US)
Article number043303
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume87
Issue number4
DOIs
StatePublished - Apr 5 2013

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Spin Glass
Ising
spin glass
Ising model
Ising Model
sampling
Nearest Neighbor
matrices
Pfaffian
Boltzmann distribution
Inverse matrix
Dimer
Ludwig Boltzmann
Partition Function
Timing
partitions
time measurement
dimers
computer programs
formulations

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability

Cite this

Numerically exact correlations and sampling in the two-dimensional Ising spin glass. / Thomas, Creighton K.; Middleton, Arthur Alan.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 87, No. 4, 043303, 05.04.2013.

Research output: Contribution to journalArticle

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