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About

This page offers a service to compute the energetic groundstates of Ising Spin Glass problems, in particular those on two- or three-dimensional regular lattices (free or periodic boundaries). For other types, the Spin Glass Server might currently be a more convenient option.

The service is offered by Daniel Faber, Petra Mutzel, and Mohamed Sonbol.

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Usage

Instances can be uploaded using the interface below. If a submitted instance is valid and of reasonable size, and if you provide a valid email-address, the instance will be passed to our solvers and either an optimal solution or, if a time limit is exceeded, intermediate results will be sent to the address specified.

The format of the results files is described in the Example output tab. Please note that this service comes without any guarantee or warranty. If you have questions, please contact mcsparse@uni-bonn.de.

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.sg Format

Please consider in addition to the specifications below that the file should have unix-style line termination (LF only) in order to support a proper handling.

A file adheres to the "sg" file format if:

(for arbitrary spin glass instances)

• It is a plain ASCII file with extension ".sg".
• Its comment lines begin with "#" and appear only at the beginning of the file.
• Its first non-comment line contains exactly two positive integers nspins and ninter in this order and separated by a single whitespace. These specify the number of spins and interactions of the defined spinglass, respectively.
• Its first non-comment line is succeeded by ninter lines that contain two positive integers sp1 and sp2, and one decimal number corr, each separated by a single whitespace. Here, sp1 and sp2 specify the two spins of the respective interaction which may be in any order, but must be different, and from the interval [1, nspins]. The entry corr specifies the correlation of the two spins. Here, a positive value indicates that the two spins are positively correlated, i.e., tend to have the same direction.
• No two of the ninter lines just prescribed refer to the same pair of spins.

Download a sample .sg instance.

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.gsg Format

Please consider in addition to the specifications below that the file should have unix-style line termination (LF only) in order to support a proper handling.

A file adheres to the "gsg" file format if:

(for grid spin glass instances)

• It it adheres to the ``sg'' file format except for that it has instead extension ``.gsg''.
• In addition, spins are indexed ascendingly row-wise on each layer from front layer to back layer.

For example, a two-dimensional (i.e., one-layer) 3x3 spin glass is numbered as follows:

                  |     |     |
                -(1)---(2)---(3)--
                  |     |     |
                -(4)---(5)---(6)--
                  |     |     |
                -(7)---(8)---(9)--
                  |     |     |
            

A three-dimensional spin glass has further layers ``behind'' that are again indexed row-wise ascendingly.

Download a sample .gsg instance.

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Output Format

The result files created by McGroundstate are in JSON format for which comfortable parsers exist in many programming languages (and which are human readable as text files besides that).

JSON format .sgs for Spin Glass Problems:

(The .sgs files feature (at least) the following information)

• If the instance was solved to optimality: The ground state energy, the ground state energy per spin, the ground state magnetization, the number of upspins, the indices of the upspins.
• Otherwise: A lower bound on the ground state energy, the energy of the best (i.e. lowest energy) spin configuration found before termination, the corresponding energy per spin and magnetization, the number of upspins in this best configuration, the indices of the upspins (starting from 1 as in the input format), and a quality measure (optimality gap) derived as $100\times \frac{|\mathrm{lower\; bound}-\mathrm{energy}|}{\mathrm{energy}}$.
• Resource information: The number of branch and cut nodes required during the solution process, and the total user and wallclock times in seconds.

Additional data may be present in the .sgs file returned.