RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 TMF: Year: Volume: Issue: Page: Find

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

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

Full text: PDF file (856 kB)
References: PDF file   HTML file

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

Bibliographic databases:

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
\Bibitem{Bas07} \by A.~G.~Basuev \paper Ising model in half-space: A series of phase transitions in low magnetic fields \jour TMF \yr 2007 \vol 153 \issue 2 \pages 220--261 \mathnet{http://mi.mathnet.ru/tmf6136} \crossref{https://doi.org/10.4213/tmf6136} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2388585} \zmath{https://zbmath.org/?q=an:1139.82309} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2007TMP...153.1539B} \elib{https://elibrary.ru/item.asp?id=10438456} \transl \jour Theoret. and Math. Phys. \yr 2007 \vol 153 \issue 2 \pages 1539--1574 \crossref{https://doi.org/10.1007/s11232-007-0132-y} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000251154200004} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-36549042560} 

• http://mi.mathnet.ru/eng/tmf6136
• https://doi.org/10.4213/tmf6136
• http://mi.mathnet.ru/eng/tmf/v153/i2/p220

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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
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
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
4. Cioletti L., Vila R., “Graphical Representations For Ising and Potts Models in General External Fields”, J. Stat. Phys., 162:1 (2016), 81–122
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
6. Ioffe D., Veleniky Y., “Low-Temperature Interfaces: Prewetting, Layering, Faceting and Ferrari - Spohn Diffusions”, Markov Process. Relat. Fields, 24:3 (2018), 487–537
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
•  Number of views: This page: 532 Full text: 148 References: 45 First page: 3