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Volumn 146, Issue 5, 2012, Pages 1059-1088

Glauber Dynamics for the Quantum Ising Model in a Transverse Field on a Regular Tree

Author keywords

Cavity equation; Glauber dynamics; Mixing time; Quantum Ising model; Spectral gap; Stochastic monotonicity

Indexed keywords


EID: 84857921275     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-012-0436-7     Document Type: Article
Times cited : (4)

References (12)
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    • Caputo, P., Martinelli, F., Simenhaus, F., Toninelli, F. L.: "Zero" temperature stochastic 3D Ising model and dimer covering fluctuations: a first step towards interface mean curvature motion. Commun. Pure Appl. Math. 64, 778-831 (2011).
    • (2011) Commun. Pure Appl. Math. , vol.64 , pp. 778-831
    • Caputo, P.1    Martinelli, F.2    Simenhaus, F.3    Toninelli, F.L.4
  • 3
    • 70350120595 scopus 로고    scopus 로고
    • Stochastic geometry of classical and quantum Ising models
    • Lecture Notes in Math, Berlin: Springer
    • Ioffe, D.: Stochastic geometry of classical and quantum Ising models. In: Methods of Contemporary Mathematical Statistical Physics. Lecture Notes in Math., vol. 1970, pp. 87-127. Springer, Berlin (2009).
    • (2009) Methods of Contemporary Mathematical Statistical Physics , vol.1970 , pp. 87-127
    • Ioffe, D.1
  • 4
    • 0000315972 scopus 로고
    • Linear operators leaving invariant a cone in a Banach space
    • Kreǐn, M. G., Rutman, M. A.: Linear operators leaving invariant a cone in a Banach space. Transl. Am. Math. Soc. 1950(26), 128 (1950).
    • (1950) Transl. Am. Math. Soc. , vol.1950 , Issue.26 , pp. 128
    • Kreǐn, M.G.1    Rutman, M.A.2
  • 5
    • 55349147372 scopus 로고    scopus 로고
    • Path-integral representation for quantum spin models: Application to the quantum cavity method and Monte Carlo simulations
    • 134428
    • Krzakala, F., Rosso, A., Semerjian, G., Zamponi, F.: Path-integral representation for quantum spin models: Application to the quantum cavity method and Monte Carlo simulations. Phys. Rev. B 78(13), 134428 (2008).
    • (2008) Phys. Rev. B , vol.78 , Issue.13
    • Krzakala, F.1    Rosso, A.2    Semerjian, G.3    Zamponi, F.4
  • 7
    • 84857924672 scopus 로고    scopus 로고
    • Quasi-polynomial mixing of the 2D stochastic Ising model with "plus" boundary up to criticality
    • (to appear). arXiv: 1012. 1271
    • Lubetzky, E., Martinelli, F., Sly, A., Toninelli, F. L.: Quasi-polynomial mixing of the 2D stochastic Ising model with "plus" boundary up to criticality. J. Eur. Math. Soc. (to appear). arXiv: 1012. 1271 (2011).
    • (2011) J. Eur. Math. Soc
    • Lubetzky, E.1    Martinelli, F.2    Sly, A.3    Toninelli, F.L.4
  • 8
    • 0001902871 scopus 로고    scopus 로고
    • Lectures on Glauber dynamics for discrete spin models
    • Saint-Flour1997Lecture Notes in Math, Berlin: Springer
    • Martinelli, F.: Lectures on Glauber dynamics for discrete spin models. In: Lectures on Probability Theory and Statistics, Saint-Flour, 1997. Lecture Notes in Math., vol. 1717, pp. 93-191. Springer, Berlin (1999).
    • (1999) Lectures on Probability Theory and Statistics , vol.1717 , pp. 93-191
    • Martinelli, F.1
  • 9
    • 70350672555 scopus 로고    scopus 로고
    • Mixing time for the solid-on-solid model
    • (to appear). arXiv: 1008. 0125, A preliminary version appeared in Proc. 41st Annual ACM Symposium on Theory of Computing, (2009)
    • Martinelli, F., Sinclair, A.: Mixing time for the solid-on-solid model. Ann. Appl. Probab. (to appear). arXiv: 1008. 0125 (2010). A preliminary version appeared in Proc. 41st Annual ACM Symposium on Theory of Computing, pp. 571-580 (2009).
    • (2010) Ann. Appl. Probab , pp. 571-580
    • Martinelli, F.1    Sinclair, A.2
  • 10
    • 77949652597 scopus 로고    scopus 로고
    • On the mixing time of the 2D stochastic Ising model with "plus" boundary conditions at low temperature
    • Martinelli, F., Toninelli, F. L.: On the mixing time of the 2D stochastic Ising model with "plus" boundary conditions at low temperature. Commun. Math. Phys. 296, 175-213 (2010).
    • (2010) Commun. Math. Phys. , vol.296 , pp. 175-213
    • Martinelli, F.1    Toninelli, F.L.2
  • 11
    • 5644296193 scopus 로고    scopus 로고
    • Glauber dynamics on trees: boundary conditions and mixing time
    • Martinelli, F., Sinclair, A., Weitz, D.: Glauber dynamics on trees: boundary conditions and mixing time. Commun. Math. Phys. 250(2), 301-334 (2004).
    • (2004) Commun. Math. Phys. , vol.250 , Issue.2 , pp. 301-334
    • Martinelli, F.1    Sinclair, A.2    Weitz, D.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.