IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v212y1994i1p194-229.html

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

    for a different version of it.

    References listed on IDEAS

    as
    1. Beale, Calvin A., "undated". "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. repec:dbl:dblbks:870 is not listed on IDEAS
    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. Hans Degryse & Steven Ongena, 2004. "The Impact of Competition on Bank Orientation and Specialization (new titel: The impact of competition on bank orientation)," CESifo Working Paper Series 1119, CESifo.
    6. Marco Alderighi & Marcella Nicolini & Claudio A. Piga, 2012. "Combined Effects of Load Factors and Booking Time on Fares: Insights from the Yield Management of a Low-Cost Airline," Quaderni di Dipartimento 171, University of Pavia, Department of Economics and Quantitative Methods.
    7. Fukui, Hideki, 2019. "How do slot restrictions affect airfares? New evidence from the US airline industry," Economics of Transportation, Elsevier, vol. 17(C), pages 51-71.
    8. Karen Ruckman & Nilesh Saraf & Vallabh Sambamurthy, 2015. "Market Positioning by IT Service Vendors Through Imitation," Information Systems Research, INFORMS, vol. 26(1), pages 100-126, March.
    9. Pham, Tho & Talavera, Oleksandr & Yang, Junhong, 2016. "Multimarket Competition and Profitability: Evidence from Ukrainian banking," MPRA Paper 72376, University Library of Munich, Germany.
    10. Anming Zhang & Yimin Zhang & Joseph A. Clougherty, 2011. "Competition and Regulation in Air Transport," Chapters, in: André de Palma & Robin Lindsey & Emile Quinet & Roger Vickerman (ed.), A Handbook of Transport Economics, chapter 35, Edward Elgar Publishing.
    11. Wehner, R.K. & Baeriswyl, D., 1975. "Equation of state of a classical anharmonic oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 81(1), pages 129-144.
    12. 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.
    13. Zhang, Yahua & Sampaio, Breno & Fu, Xiaowen & Huang, Zhibin, 2018. "Pricing dynamics between airline groups with dual-brand services," Transportation Research Part A: Policy and Practice, Elsevier, vol. 112(C), pages 46-59.
    14. Cantillo, Miguel, 2016. "Villains or Heroes? Private Banks and Railroads after the Sherman Act," MPRA Paper 79354, University Library of Munich, Germany.
    15. Tho Pham & Oleksandr Talavera & Junhong Yang, 2020. "Multimarket competition and profitability: evidence from Ukrainian banks," Oxford Economic Papers, Oxford University Press, vol. 72(2), pages 517-545.
    16. Stephen Martin, 2012. "Market Structure and Market Performance," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 40(2), pages 87-108, March.
    17. Sebastian Linde & Ralph Siebert, 2016. "Do Mergers Among Multimarket Firms Create Value?," CESifo Working Paper Series 6139, CESifo.
    18. Srabana Gupta, 2001. "The Effect of Bid Rigging on Prices: A Study of the Highway Construction Industry," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 19(4), pages 451-465, December.
    19. Degryse, Hans & Ongena, Steven, 2007. "The impact of competition on bank orientation," Journal of Financial Intermediation, Elsevier, vol. 16(3), pages 399-424, July.
    20. 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.

    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.