IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v184y1992i3p493-498.html
   My bibliography  Save this article

Blocking transitions in lattice spin models with directed kinetic constraints

Author

Listed:
  • Reiter, Johannes
  • Mauch, Franz
  • Jäckle, Josef

Abstract

We present a class of kinetic Ising models with a directed constraint, which exhibit a dynamocal phase transition at a critical up-spin concentration. At lower up-spin concentrations a non-ergodic state exists, for which the fraction of permanently blocked spins plays the role of an order parameter. The spin autocorrelation function has been calculated by Monte Carlo simulation for two particular models: One for the square lattice, with the constraint that the neighboring spins in the north and in the east are up, and one for a Cayley tree with branching ratio 2, where both neighbors above a given spin must be up. The transition is of second order, and the integrated autocorrelation time diverges on both sides of the transition. The models define a distribution of blocking lengths, which can be calculated analytically for the Cayley tree. We conjecture that this length distribution is related to the autocorrelation time by a dynamic critical exponent, which is numerically estimated for small lattices up to a length 11 to be about 5 and 2.7 for the two models, respectively.

Suggested Citation

  • Reiter, Johannes & Mauch, Franz & Jäckle, Josef, 1992. "Blocking transitions in lattice spin models with directed kinetic constraints," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 184(3), pages 493-498.
    • Handle: RePEc:eee:phsmap:v:184:y:1992:i:3:p:493-498
    DOI: 10.1016/0378-4371(92)90319-L
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/037843719290319L
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/0378-4371(92)90319-L?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Stanley J. Benkoski & Michael G. Monticino & James R. Weisinger, 1991. "A survey of the search theory literature," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(4), pages 469-494, August.
    2. repec:ilo:ilowps:251095 is not listed on IDEAS
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Steven M. Shechter & Farhad Ghassemi & Yasin Gocgun & Martin L. Puterman, 2015. "Technical Note—Trading Off Quick versus Slow Actions in Optimal Search," Operations Research, INFORMS, vol. 63(2), pages 353-362, April.
    2. T. C. E. Cheng & B. Kriheli & E. Levner & C. T. Ng, 2021. "Scheduling an autonomous robot searching for hidden targets," Annals of Operations Research, Springer, vol. 298(1), pages 95-109, March.
    3. Hoam Chung & Elijah Polak & Johannes O. Royset & Shankar Sastry, 2011. "On the optimal detection of an underwater intruder in a channel using unmanned underwater vehicles," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(8), pages 804-820, December.
    4. Frédéric Dambreville & Jean‐Pierre Le Cadre, 2002. "Detection of a Markovian target with optimization of the search efforts under generalized linear constraints," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(2), pages 117-142, March.
    5. Benoit Duvocelle & János Flesch & Hui Min Shi & Dries Vermeulen, 2021. "Search for a moving target in a competitive environment," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(2), pages 547-557, June.
    6. Gregg S. Gonsalves & Forrest W. Crawford & Paul D. Cleary & Edward H. Kaplan & A. David Paltiel, 2018. "An Adaptive Approach to Locating Mobile HIV Testing Services," Medical Decision Making, , vol. 38(2), pages 262-272, February.
    7. Reiter, J. & Jäckle, J., 1995. "Dynamics of the symmetrically constrained Ising chain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 215(3), pages 311-330.
    8. Abd-Elmoneim Anwar Mohamed & Mohamed Abd Allah El-Hadidy, 2013. "Optimal Multiplicative Generalized Linear Search Plan for a Discrete Random Walker," Journal of Optimization, Hindawi, vol. 2013, pages 1-13, July.
    9. Steve Alpern, 2002. "Rendezvous Search: A Personal Perspective," Operations Research, INFORMS, vol. 50(5), pages 772-795, October.
    10. Joseph B. Kadane, 2015. "Optimal discrete search with technological choice," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 81(3), pages 317-336, June.
    11. Timothy H. Chung & Rachel T. Silvestrini, 2014. "Modeling and analysis of exhaustive probabilistic search," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(2), pages 164-178, March.
    12. Delavernhe, Florian & Jaillet, Patrick & Rossi, André & Sevaux, Marc, 2021. "Planning a multi-sensors search for a moving target considering traveling costs," European Journal of Operational Research, Elsevier, vol. 292(2), pages 469-482.
    13. Johannes O. Royset & Hiroyuki Sato, 2010. "Route optimization for multiple searchers," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(8), pages 701-717, December.
    14. Duvocelle, Benoit & Flesch, János & Staudigl, Mathias & Vermeulen, Dries, 2022. "A competitive search game with a moving target," European Journal of Operational Research, Elsevier, vol. 303(2), pages 945-957.
    15. Endre Csóka & Thomas Lidbetter, 2016. "The solution to an open problem for a caching game," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(1), pages 23-31, February.
    16. Frédéric Dambreville & Jean‐Pierre Le Cadre, 2007. "Constrained minimax optimization of continuous search efforts for the detection of a stationary target," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(6), pages 589-601, September.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:184:y:1992:i:3:p:493-498. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.