IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v246y1997i1p253-274.html

Repulsive particles on a two-dimensional lattice

Author

Listed:
  • Watson, G.I.

Abstract

The problem of finding the minimum-energy configurations of particles on a square lattice, subject to short-ranged repulsive interactions, is studied analytically. The study is relevant to charge-ordered states of interacting fermions, as described by the spinless Falicov-Kimball model. A simple model is introduced, corresponding to the limit of a two-body potential which is a very rapidly decreasing convex function of distance. Its ground states are found rigorously for certain density ranges, including half filling. These agree with known properties of neutral ground states of the large-U Falicov-Kimball model, suggesting a characterization of the latter as “most homogeneous” configurations. For lower densities, a family of ground states is found having the novel property that they are aperiodic even when the particle density is a rational number. In some cases, local phase separation suggests an inherent sensitivity to the detailed form of the interaction potential.

Suggested Citation

  • Watson, G.I., 1997. "Repulsive particles on a two-dimensional lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(1), pages 253-274.
    • Handle: RePEc:eee:phsmap:v:246:y:1997:i:1:p:253-274
    DOI: 10.1016/S0378-4371(97)00349-X
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037843719700349X
    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/S0378-4371(97)00349-X?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Shane, Scott & Kolvereid, Lars & Westhead, Paul, 1991. "An exploratory examination of the reasons leading to new firm formation across country and gender," Journal of Business Venturing, Elsevier, vol. 6(6), pages 431-446, November.
    2. repec:cup:jechis:v:29:y:1969:i:04:p:758-772_07 is not listed on IDEAS
    3. Macris, N., 1996. "Periodic ground states in simple models of itinerant fermions interacting with classical fields," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 232(3), pages 648-656.
    4. Miracle-Solé, S., 1996. "A study of the large coupling expansion in the Falicov-Kimball model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 232(3), pages 686-701.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Derzhko, Volodymyr & Jȩdrzejewski, Janusz, 2003. "From phase separation to long-range order in a system of interacting electrons," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 328(3), pages 449-465.

    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. Darja Reuschke, 2019. "The subjective well-being of homeworkers across life domains," Environment and Planning A, , vol. 51(6), pages 1326-1349, September.
    2. Peter Zwan & Roy Thurik & Ingrid Verheul & Jolanda Hessels, 2016. "Erratum to: Factors influencing the entrepreneurial engagement of opportunity and necessity entrepreneurs," Eurasian Business Review, Springer;Eurasia Business and Economics Society, vol. 6(3), pages 297-297, December.
    3. António Porfírio, José & Augusto Felício, José & Carrilho, Tiago & Jardim, Jacinto, 2023. "Promoting entrepreneurial intentions from adolescence: The influence of entrepreneurial culture and education," Journal of Business Research, Elsevier, vol. 156(C).
    4. Westhead, Paul & Wright, Mike, 1998. "Novice, portfolio, and serial founders: are they different?," Journal of Business Venturing, Elsevier, vol. 13(3), pages 173-204, May.
    5. Paul A. Coomes & Jose Fernandez & Stephan F. Gohmann, 2013. "The Rate of Proprietorship Among Metropolitan Areas: The Impact of the Local Economic Environment and Capital Resources," Entrepreneurship Theory and Practice, , vol. 37(4), pages 745-770, July.
    6. Jones, Marian V. & Coviello, Nicole & Tang, Yee Kwan, 2011. "International Entrepreneurship research (1989–2009): A domain ontology and thematic analysis," Journal of Business Venturing, Elsevier, vol. 26(6), pages 632-659.
    7. Emmanuel Affum-Osei & Sharon G. Goto & June Chun Yeung & Rong Wang & Hodar Lam & Inusah Abdul-Nasiru & Darius K. S. Chan, 2024. "A cross-cultural study of entrepreneurial motivation and entrepreneurial intentions amongst university students: the roles of individualism and collectivism," Journal of Global Entrepreneurship Research, Springer;UNESCO Chair in Entrepreneurship, vol. 14(1), pages 1-19, December.
    8. José Luis Crespo-Espert & Antonio García-Tabuenca & Federico Pablo-Martí, 2012. "Women, entrepreneurial activity and territory: differences or myths?," Chapters, in: Charlie Karlsson & Börje Johansson & Roger R. Stough (ed.), Entrepreneurship, Social Capital and Governance, chapter 6, pages 115-159, Edward Elgar Publishing.
    9. Thang Nguyen & Lan Nguyen & Scott Bryant & Hieu Nguyen, 2020. "What Motivates Scientists in Emerging Economies to Become Entrepreneurs? Evidence from Vietnam," Sustainability, MDPI, vol. 12(3), pages 1-18, February.
    10. Ingrid Verheul & André Van Stel & Roy Thurik, 2006. "Explaining female and male entrepreneurship at the country level," Entrepreneurship & Regional Development, Taylor & Francis Journals, vol. 18(2), pages 151-183, March.
    11. Mirko Hirschmann & Christian Fisch & Steffen Farny, 2025. "An attention-based perspective on how climate impact affects opportunity entrepreneurship," Small Business Economics, Springer, vol. 65(4), pages 2217-2257, December.
    12. Thurik, A. Roy & Carree, Martin A. & van Stel, André & Audretsch, David B., 2008. "Does self-employment reduce unemployment?," Journal of Business Venturing, Elsevier, vol. 23(6), pages 673-686, November.
    13. Mauricio Andrés Ramírez Gómez, 2013. "Instituciones informales y actividad emprendedora. Una aproximación metodológica desde D. North," Revista Ciencias Estratégicas, Universidad Pontificia Bolivariana.
    14. James Hayton & Gabriella Cacciotti, 2014. "Is there an entrepreneurial culture? A review of empirical research," Research Papers 0016, Enterprise Research Centre.
    15. Saeed Saadat & Muffatto Moreno & Yousafzai Shumaila, 2014. "A Multi-level Study of Entrepreneurship Education among Pakistani University Students," Entrepreneurship Research Journal, De Gruyter, vol. 4(3), pages 297-321, July.
    16. Daniel V. Holland & Dean A. Shepherd, 2013. "Deciding to Persist: Adversity, Values, and Entrepreneurs’ Decision Policies," Entrepreneurship Theory and Practice, , vol. 37(2), pages 331-358, March.
    17. Per Davidsson & Johan Wiklund, 2009. "Scott A. Shane: winner of the Global Award for Entrepreneurship Research," Small Business Economics, Springer, vol. 33(2), pages 131-140, August.
    18. Kevin Banning* & Ravi Chinta, 2019. "Attitudinal and Structural Determinants of Entrepreneurial Intentions of Women," Business, Management and Economics Research, Academic Research Publishing Group, vol. 5(2), pages 26-32, 02-2019.
    19. Ioannis Giotopoulos & Alexandra Kontolaimou & Aggelos Tsakanikas, 2017. "Drivers of high-quality entrepreneurship: what changes did the crisis bring about?," Small Business Economics, Springer, vol. 48(4), pages 913-930, April.
    20. Helene Ahl & Karin Berglund & Katarina Pettersson & Malin Tillmar, 2016. "From feminism to FemInc.ism: On the uneasy relationship between feminism, entrepreneurship and the Nordic welfare state," International Entrepreneurship and Management Journal, Springer, vol. 12(2), pages 369-392, June.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    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:246:y:1997:i:1:p:253-274. 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.