Corpus ID: 219402016

Describing classical spin Hamiltonians as automata: a new complexity measure

@article{Drexel2020DescribingCS,
  title={Describing classical spin Hamiltonians as automata: a new complexity measure},
  author={David Drexel and Gemma de las Cuevas},
  journal={arXiv: Statistical Mechanics},
  year={2020}
}
  • David Drexel, Gemma de las Cuevas
  • Published 2020
  • Mathematics, Physics
  • arXiv: Statistical Mechanics
  • We introduce a new complexity measure of classical spin Hamiltonians in which they are described as automata. Specifically, we associate a classical spin Hamiltonians to the formal language consisting of pairs of spin configurations and the corresponding energy, and classify this language in the Chomsky hierarchy. We prove that one-dimensional (1D) local classical spin Hamiltonians correspond to deterministic pushdown automata, and the two-dimensional (2D) case corresponds to linear bounded… CONTINUE READING

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    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 10 REFERENCES

    2D Ising model with fields is equivalent to the 2D Ising model without fields on a square lattice with an additional 'spike', that is, an outlying extra vertex connected to every other vertex

    45

    • T. Cubitt, A. Montanaro, SIAM J. Comput
    • 268
    • 2016
    VIEW 1 EXCERPT

    A 15

    • F. Barahona, J. Phys
    • 3241
    • 1982
    VIEW 2 EXCERPTS

    JSTAT 176

    • T. Kohler, T. S. Cubitt
    • 228
    • 2019
    VIEW 1 EXCERPT

    Proc

    • T. S. Cubitt, A. Montanaro, S. Piddock
    • Natl. Acad. Sci. 38, 9497
    • 2018
    VIEW 1 EXCERPT

    The nature of computation (Oxford

    • C. Moore, S. Mertens
    • 2011
    VIEW 1 EXCERPT

    We conjecture that any other transformation whose description is independent of the system size would result in a formal language at the same level of the Chomsky hierarchy

    We take this energy value to be rational number, so that we can later rescale it to h ′ , whose image are natural numbers

    and T

    • T. Kohler, S. Piddock, J. Bausch
    • Cubitt,
    VIEW 1 EXCERPT