IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v212y1994i1p194-229.html
   My bibliography  Save this article

Application of a constrained-transfer-matrix method to metastability in the d = 2 Ising ferromagnet

Author

Listed:
  • Günther, C.C.A.
  • Rikvold, P.A.
  • Novotny, M.A.

Abstract

Applying a numerical transfer-matrix formalism, we obtained complex-valued constrained free energies for the two-dimensional square-lattice nearest-neighbor Ising ferromagnet below its critical temperature and in an external magnetic field. In particular, we study the imaginary part of the constrained free-energy branch that corresponds to the metastable phase. Although droplets are not introduced explicitly, the metastable free energy is obtained in excellent agreement with field-theoretical droplet-model predictions. The finite-size scaling properties are different in the weak-field and intermediate-field regimes, and we identify the corresponding different critical-droplet shapes. For intermediate fields, we show that the surface free energy of the critical droplet is given by a Wuff construction with the equilibrium surface tension. We also find a prefactor exponent in complete agreement with the field-theoretical droplet model. Our results extend the region of validity for known results of this field-theoretical droplet model, and they indicate that this transfer-matrix approach provides a nonperturbative numerical continuation of the equilibrium free energy into the metastable phase.

Suggested Citation

  • Günther, C.C.A. & Rikvold, P.A. & Novotny, M.A., 1994. "Application of a constrained-transfer-matrix method to metastability in the d = 2 Ising ferromagnet," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 212(1), pages 194-229.
    • Handle: RePEc:eee:phsmap:v:212:y:1994:i:1:p:194-229
    DOI: 10.1016/0378-4371(94)90147-3
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0378437194901473
    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(94)90147-3?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. Beale, Calvin A., 1990. "Reflections on Rural Demography, Rural Society, and Predicting Social Behavior," AE & RS Research Reports 257710, Pennsylvania State University, Department of Agricultural Economics and Rural Sociology.
    2. Emmons, K.M. & Abrams, D.B. & Marshall, R.J. & Etzel, R.A. & Novotny, T.E. & Marcus, B.H. & Kane, M.E., 1992. "Exposure to environmental tobacco smoke in naturalistic settings," American Journal of Public Health, American Public Health Association, vol. 82(1), pages 24-28.
    3. Escorche, Victor & Gomez Bravo, Luis & Guzman, Jorge & Medina, Ernesto & Paez, Tomás & Rodriguez, Francisco & Tamayo, Francisco & Valera, Nabors, . "Productividad y calidad. Manual del consultor," Books, CAF Development Bank Of Latinamerica, number 870.
    4. Stoll, Hans R, 1973. "The Relationship Between Put and Call Option Prices: Reply," Journal of Finance, American Finance Association, vol. 28(1), pages 185-187, March.
    5. Cassell, E.J. & Lebowitz, M.D. & Wolter, D.W. & McCarroll, J.R., 1971. "Health and the urban environment. IX. The concept of the multiplex independent variable," American Journal of Public Health, American Public Health Association, vol. 61(12), pages 2348-2353.
    6. William N. Evans & Ioannis N. Kessides, 1994. "Living by the "Golden Rule": Multimarket Contact in the U. S. Airline Industry," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 109(2), pages 341-366.
    7. Schulman, L.S., 1977. "Phase transitions with several order parameters," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 89(3), pages 597-604.
    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. Kaplow, Louis & Shapiro, Carl, 2007. "Antitrust," Handbook of Law and Economics, in: A. Mitchell Polinsky & Steven Shavell (ed.), Handbook of Law and Economics, edition 1, volume 2, chapter 15, pages 1073-1225, Elsevier.
    2. Faouzi Bensebaa, 2003. "La dynamique concurrentielle:défis analytiques et méthodologiques," Revue Finance Contrôle Stratégie, revues.org, vol. 6(1), pages 5-37, March.
    3. Maria José Gil-Moltó & Claudio A. Piga, 2007. "Entry and Exit in a Liberalised Market," Rivista di Politica Economica, SIPI Spa, vol. 97(1), pages 3-38, January-F.
    4. Gayle, Philip G. & Wu, Chi-Yin, 2013. "A re-examination of incumbents’ response to the threat of entry: Evidence from the airline industry," Economics of Transportation, Elsevier, vol. 2(4), pages 119-130.
    5. Pham, Tho & Talavera, Oleksandr & Yang, Junhong, 2016. "Multimarket Competition and Profitability: Evidence from Ukrainian banking," MPRA Paper 72376, University Library of Munich, Germany.
    6. Madeleine Besson & Bernard Bourdon, 2015. "Can multimarket competition theory explain why manufacturers are reluctant to adopt e-commerce ? The case of the French household appliances’ manufacturers," Grenoble Ecole de Management (Post-Print) hal-02387337, HAL.
    7. Javier Coronado & Sergi Jiménez-Martín & Pedro L. Marín, 2007. "Multimarket contact in pharmaceutical markets," Economics Working Papers 1033, Department of Economics and Business, Universitat Pompeu Fabra, revised Jul 2007.
    8. Stephen Martin, 2012. "Market Structure and Market Performance," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 40(2), pages 87-108, March.
    9. Sebastian Linde & Ralph Siebert, 2016. "Do Mergers Among Multimarket Firms Create Value?," CESifo Working Paper Series 6139, CESifo.
    10. Bamberger, Gustavo E & Carlton, Dennis W & Neumann, Lynette R, 2004. "An Empirical Investigation of the Competitive Effects of Domestic Airline Alliances," Journal of Law and Economics, University of Chicago Press, vol. 47(1), pages 195-222, April.
    11. Degryse, Hans & Ongena, Steven, 2007. "The impact of competition on bank orientation," Journal of Financial Intermediation, Elsevier, vol. 16(3), pages 399-424, July.
    12. Ciliberto, Federico & Williams, Jonathan, 2010. "Does Multimarket Contact Facilitate Tacit Collusion? Inference on Conjectural Parameters in the Airline Industry," MPRA Paper 24888, University Library of Munich, Germany.
    13. Haizhen Lin & Ian M. McCarthy, 2023. "Multimarket Contact in Health Insurance: Evidence from Medicare Advantage," Journal of Industrial Economics, Wiley Blackwell, vol. 71(1), pages 212-255, March.
    14. Javier Gimeno, 2002. "The performance effects of unintended and purposive multimarket contact," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 23(4-5), pages 209-224.
    15. de Haas, Ralph & Lu, Liping & Ongena, S.R.G., 2018. "Clear and Close Competitors? : On the Causes and Consequences of Bilateral Competition between Banks," Other publications TiSEM e9f86045-13c5-49d9-85df-1, Tilburg University, School of Economics and Management.
    16. Brueckner, Jan K. & Lee, Darin & Singer, Ethan S., 2013. "Airline competition and domestic US airfares: A comprehensivereappraisal," Economics of Transportation, Elsevier, vol. 2(1), pages 1-17.
    17. Yahua Zhang & David Round, 2009. "Policy Implications of the Effects of Concentration and Multimarket Contact in China’s Airline Market," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 34(4), pages 307-326, June.
    18. Domanico, Fabio, 2007. "Concentration in the European electricity industry: The internal market as solution?," Energy Policy, Elsevier, vol. 35(10), pages 5064-5076, October.
    19. de Leverano, Adriano, 2019. "Collusion through market sharing agreements: Evidence from Quebec's road paving market," ZEW Discussion Papers 19-053, ZEW - Leibniz Centre for European Economic Research.
    20. Arie, Guy & Markovich, Sarit & Varela, Mauricio, 2017. "On the competitive effects of multimarket contact," European Economic Review, Elsevier, vol. 100(C), pages 116-142.

    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:212:y:1994:i:1:p:194-229. 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.