Ultraslow dynamics in a translationally invariant spin model for multiplication and factorization
We construct a model of short-range interacting Ising spins on a translationally invariant two-dimensional lattice that mimics a reversible circuit that multiplies or factorizes integers, depending on the choice of boundary conditions. We prove that, for open boundary conditions, the model exhibits...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2019-10-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.1.033001 |
| _version_ | 1797211706776092672 |
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| author | Lei Zhang Stefanos Kourtis Claudio Chamon Eduardo R. Mucciolo Andrei E. Ruckenstein |
| author_facet | Lei Zhang Stefanos Kourtis Claudio Chamon Eduardo R. Mucciolo Andrei E. Ruckenstein |
| author_sort | Lei Zhang |
| collection | DOAJ |
| description | We construct a model of short-range interacting Ising spins on a translationally invariant two-dimensional lattice that mimics a reversible circuit that multiplies or factorizes integers, depending on the choice of boundary conditions. We prove that, for open boundary conditions, the model exhibits no finite-temperature phase transition. Yet we find that it displays glassy dynamics with astronomically slow relaxation times, numerically consistent with a double exponential dependence on the inverse temperature. The slowness of the dynamics arises due to errors that occur during thermal annealing that cost little energy but flip an extensive number of spins. We argue that the energy barrier that needs to be overcome in order to heal such defects scales linearly with the correlation length, which diverges exponentially with inverse temperature, thus yielding the double exponential behavior of the relaxation time. |
| first_indexed | 2024-04-24T10:30:45Z |
| format | Article |
| id | doaj.art-eb845f87d1764fe888ed35ab76630d4c |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:30:45Z |
| publishDate | 2019-10-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-eb845f87d1764fe888ed35ab76630d4c2024-04-12T16:45:53ZengAmerican Physical SocietyPhysical Review Research2643-15642019-10-011303300110.1103/PhysRevResearch.1.033001Ultraslow dynamics in a translationally invariant spin model for multiplication and factorizationLei ZhangStefanos KourtisClaudio ChamonEduardo R. MuccioloAndrei E. RuckensteinWe construct a model of short-range interacting Ising spins on a translationally invariant two-dimensional lattice that mimics a reversible circuit that multiplies or factorizes integers, depending on the choice of boundary conditions. We prove that, for open boundary conditions, the model exhibits no finite-temperature phase transition. Yet we find that it displays glassy dynamics with astronomically slow relaxation times, numerically consistent with a double exponential dependence on the inverse temperature. The slowness of the dynamics arises due to errors that occur during thermal annealing that cost little energy but flip an extensive number of spins. We argue that the energy barrier that needs to be overcome in order to heal such defects scales linearly with the correlation length, which diverges exponentially with inverse temperature, thus yielding the double exponential behavior of the relaxation time.http://doi.org/10.1103/PhysRevResearch.1.033001 |
| spellingShingle | Lei Zhang Stefanos Kourtis Claudio Chamon Eduardo R. Mucciolo Andrei E. Ruckenstein Ultraslow dynamics in a translationally invariant spin model for multiplication and factorization Physical Review Research |
| title | Ultraslow dynamics in a translationally invariant spin model for multiplication and factorization |
| title_full | Ultraslow dynamics in a translationally invariant spin model for multiplication and factorization |
| title_fullStr | Ultraslow dynamics in a translationally invariant spin model for multiplication and factorization |
| title_full_unstemmed | Ultraslow dynamics in a translationally invariant spin model for multiplication and factorization |
| title_short | Ultraslow dynamics in a translationally invariant spin model for multiplication and factorization |
| title_sort | ultraslow dynamics in a translationally invariant spin model for multiplication and factorization |
| url | http://doi.org/10.1103/PhysRevResearch.1.033001 |
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