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TMF, 2007, Volume 153, Number 2, Pages 220–261 (Mi tmf6136)  

This article is cited in 7 scientific papers (total in 7 papers)

Ising model in half-space: A series of phase transitions in low magnetic fields

A. G. Basuev

St. Petersburg State University of Technology and Design

Abstract: For the Ising model in half-space at low temperatures and for the “unstable boundary condition,” we prove that for each value of the external magnetic field $\mu$, there exists a spin layer of thickness $q(\mu)$ adjacent to the substrate such that the mean spin is close to $-1$ inside this layer and close to $+1$ outside it. As $\mu$ decreases, the thickness of the $(-1)$-spin layer changes jumpwise by unity at the points $\mu_q$, and $q(\mu)\to\infty$ as $\mu\to+0$. At the discontinuity points $\mu_q$ of $q(\mu)$, two surface phases coexist. The surface free energy is piecewise analytic in the domain $\operatorname{Re}\mu>0$ and at low temperatures. We consider the Ising model in half-space with an arbitrary external field in the zeroth layer and investigate the corresponding phase diagram. We prove Antonov's rule and construct the equation of state in lower orders with the precision of $x^7$, $x=e^{-2\varepsilon}$. In particular, with this precision, we find the points of coexistence of the phases $0,1,2$ and the phases $0,2,3$, where the phase numbers correspond to the height of the layer of unstable spins over the substrate.

DOI: https://doi.org/10.4213/tmf6136

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English version:
Theoretical and Mathematical Physics, 2007, 153:2, 1539–1574

Bibliographic databases:

Received: 29.09.2006
Revised: 20.03.2007

Citation: A. G. Basuev, “Ising model in half-space: A series of phase transitions in low magnetic fields”, TMF, 153:2 (2007), 220–261; Theoret. and Math. Phys., 153:2 (2007), 1539–1574

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Alexander K.S., Dunlop F., Miracle-Sole S., “Layering in the Ising Model”, J Stat Phys, 141:2 (2010), 217–241  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. Bissacot R., Cioletti L., “Phase Transition in Ferromagnetic Ising Models with Non-uniform External Magnetic Fields”, J Stat Phys, 139:5 (2010), 769–778  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. Alexander K.S., Dunlop F., Miracle-Sole S., “Layering and Wetting Transitions for an SOS Interface”, J Stat Phys, 142:3 (2011), 524–576  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    4. Cioletti L., Vila R., “Graphical Representations For Ising and Potts Models in General External Fields”, J. Stat. Phys., 162:1 (2016), 81–122  crossref  mathscinet  zmath  adsnasa  isi  scopus
    5. Crawford N., De Roeck W., “Stability of the Uniqueness Regime For Ferromagnetic Glauber Dynamics Under Non-Reversible Perturbations”, Ann. Henri Poincare, 19:9 (2018), 2651–2671  crossref  mathscinet  zmath  isi  scopus
    6. Ioffe D., Veleniky Y., “Low-Temperature Interfaces: Prewetting, Layering, Faceting and Ferrari - Spohn Diffusions”, Markov Process. Relat. Fields, 24:3 (2018), 487–537  mathscinet  zmath  isi
    7. Abraham D., Newman Ch.M., Shlosman S., “A Continuum of Pure States in the Ising Model on a Halfplane”, J. Stat. Phys., 172:2, SI (2018), 611–626  crossref  mathscinet  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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