메뉴 건너뛰기




Volumn 147, Issue 2, 2012, Pages 315-350

Geometric Exponents of Dilute Loop Models

Author keywords

Conformal field theory; Conformal loop ensembles; Dilute loop models; Fractal dimensions; Geometric exponents; Logarithmic minimal models; Monte Carlo simulations; SLE

Indexed keywords


EID: 84860383802     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-012-0464-3     Document Type: Article
Times cited : (9)

References (41)
  • 1
    • 77950203311 scopus 로고    scopus 로고
    • Fractal dimensions of the Q-state Potts model for the complete and external hulls
    • arXiv: 1001. 0055v1 [cond-mat. stat-mech]
    • Adams, D. A., Sander, L. M., Ziff, R. M.: Fractal dimensions of the Q-state Potts model for the complete and external hulls. J. Stat. Mech. P03004 (2010). arXiv: 1001. 0055v1 [cond-mat. stat-mech].
    • (2010) J. Stat. Mech.
    • Adams, D.A.1    Sander, L.M.2    Ziff, R.M.3
  • 2
    • 0037316511 scopus 로고    scopus 로고
    • Fractal dimensions and corrections to scaling for critical Potts clusters
    • arXiv:cond-mat/0206367
    • Aharony, A., Asikainen, J.: Fractal dimensions and corrections to scaling for critical Potts clusters. Fractals 11, 3-7 (2003). arXiv: cond-mat/0206367.
    • (2003) Fractals , vol.11 , pp. 3-7
    • Aharony, A.1    Asikainen, J.2
  • 3
    • 0141561957 scopus 로고    scopus 로고
    • Homology of Fortuin-Kasteleyn clusters of Potts models on the torus
    • arXiv:hep-th/0111193
    • Arguin, L.-P.: Homology of Fortuin-Kasteleyn clusters of Potts models on the torus. J. Stat. Phys. 109, 301-310 (2002). arXiv: hep-th/0111193.
    • (2002) J. Stat. Phys. , vol.109 , pp. 301-310
    • Arguin, L.-P.1
  • 5
    • 0000663210 scopus 로고
    • Exact results for Hamiltonian walks from the solution of the fully packed loop model on the honeycomb lattice
    • arXiv:cond-mat/9408083v1
    • Batchelor, M. T., Suzuki, J., Yung, C. M.: Exact results for Hamiltonian walks from the solution of the fully packed loop model on the honeycomb lattice. Phys. Rev. Lett. 73, 2646-2649 (1994). arXiv: cond-mat/9408083v1.
    • (1994) Phys. Rev. Lett. , vol.73 , pp. 2646-2649
    • Batchelor, M.T.1    Suzuki, J.2    Yung, C.M.3
  • 6
    • 52049084572 scopus 로고    scopus 로고
    • The dimension of the SLE curves
    • arXiv:math/0211322v3 [math.PR]
    • Beffara, V.: The dimension of the SLE curves. Ann. Probab. 36(4), 1421-1452 (2008). arXiv: math/0211322v3 [math. PR].
    • (2008) Ann. Probab. , vol.36 , Issue.4 , pp. 1421-1452
    • Beffara, V.1
  • 7
    • 0040239364 scopus 로고
    • Critical behaviour and conformal anomaly of the O(n) model on the square lattice
    • Blöte, H. W. J., Nienhuis, B.: Critical behaviour and conformal anomaly of the O(n) model on the square lattice. J. Phys. A, Math. Gen. 22, 1415-1438 (1989).
    • (1989) J. Phys. A, Math. Gen. , vol.22 , pp. 1415-1438
    • Blöte, H.W.J.1    Nienhuis, B.2
  • 8
    • 2342578042 scopus 로고
    • Geometrical aspects of critical Ising configurations in two dimensions
    • Blöte, H. W. J., Knops, Y. M. M., Nienhuis, B.: Geometrical aspects of critical Ising configurations in two dimensions. Phys. Rev. Lett. 68, 3440-3443 (1992).
    • (1992) Phys. Rev. Lett. , vol.68 , pp. 3440-3443
    • Blöte, H.W.J.1    Knops, Y.M.M.2    Nienhuis, B.3
  • 9
    • 33749356449 scopus 로고    scopus 로고
    • Two-dimensional critical percolation: the full scaling limit
    • arXiv:math/0605035v1 [math.PR]
    • Camia, F., Newman, C. M.: Two-dimensional critical percolation: the full scaling limit. Commun. Math. Phys. 268, 1-38 (2006). arXiv: math/0605035v1 [math. PR].
    • (2006) Commun. Math. Phys. , vol.268 , pp. 1-38
    • Camia, F.1    Newman, C.M.2
  • 10
    • 0032097196 scopus 로고    scopus 로고
    • Graphical representations and cluster algorithms II
    • Chayes, L., Machta, J.: Graphical representations and cluster algorithms II. Physica A 254, 477-516 (1998).
    • (1998) Physica A , vol.254 , pp. 477-516
    • Chayes, L.1    Machta, J.2
  • 11
    • 0001285996 scopus 로고
    • Fractal structure of Ising and Potts clusters: exact results
    • Coniglio, A.: Fractal structure of Ising and Potts clusters: exact results. Phys. Rev. Lett. 62, 3054-3057 (1989).
    • (1989) Phys. Rev. Lett. , vol.62 , pp. 3054-3057
    • Coniglio, A.1
  • 12
    • 42749107610 scopus 로고    scopus 로고
    • Geometric properties of two-dimensional critical and tricritical Potts models
    • Deng, Y., Blöte, H. W. J., Nienhuis, B.: Geometric properties of two-dimensional critical and tricritical Potts models. Phys. Rev. E 69, 026123 (2004).
    • (2004) Phys. Rev. E , vol.69 , pp. 026123
    • Deng, Y.1    Blöte, H.W.J.2    Nienhuis, B.3
  • 13
    • 33947502902 scopus 로고    scopus 로고
    • Cluster simulations of loop models on two-dimensional lattices
    • 120601arXiv:cond-mat/0608447v3 [cond-mat.stat-mech]
    • Deng, Y., Garoni, T. M., Guo, W., Blöte, H. W. J., Sokal, A. D.: Cluster simulations of loop models on two-dimensional lattices. Phys. Rev. Lett. 98, 120601 (2007). arXiv: cond-mat/0608447v3 [cond-mat. stat-mech].
    • (2007) Phys. Rev. Lett. , vol.98
    • Deng, Y.1    Garoni, T.M.2    Guo, W.3    Blöte, H.W.J.4    Sokal, A.D.5
  • 14
    • 67650157167 scopus 로고    scopus 로고
    • Geometric properties of two-dimensional O(n) loop configurations
    • arXiv:cond-mat/0608547v1 [cond-mat.stat.mech]
    • Ding, C., Deng, Y., Guo, W., Qian, X., Blöte, H. W. J.: Geometric properties of two-dimensional O(n) loop configurations. J. Phys. A, Math. Theor. 40, 3305-3317 (2007). arXiv: cond-mat/0608547v1 [cond-mat. stat. mech].
    • (2007) J. Phys. A, Math. Theor. , vol.40 , pp. 3305-3317
    • Ding, C.1    Deng, Y.2    Guo, W.3    Qian, X.4    Blöte, H.W.J.5
  • 16
    • 71849096540 scopus 로고    scopus 로고
    • Conformal boundary conditions in the critical O(n) model and dilute loop models
    • arXiv:0905.1382v1
    • Dubail, J., Jacobsen, J. L., Saleur, H.: Conformal boundary conditions in the critical O(n) model and dilute loop models. Nucl. Phys. B 827, 457-502 (2010). arXiv: 0905. 1382v1.
    • (2010) Nucl. Phys. B , vol.827 , pp. 457-502
    • Dubail, J.1    Jacobsen, J.L.2    Saleur, H.3
  • 18
    • 0001206927 scopus 로고
    • Critical exponents of Manhattan Hamiltonian walks in two dimensions, from Potts and O(n) models
    • Duplantier, B.: Critical exponents of Manhattan Hamiltonian walks in two dimensions, from Potts and O(n) models. J. Stat. Phys. 49, 411-431 (1987).
    • (1987) J. Stat. Phys. , vol.49 , pp. 411-431
    • Duplantier, B.1
  • 19
    • 0345973045 scopus 로고
    • Two-dimensional fractal geometry, critical phenomena and conformal invariance
    • Duplantier, B.: Two-dimensional fractal geometry, critical phenomena and conformal invariance. Phys. Rep. 184(2-4), 229-257 (1989).
    • (1989) Phys. Rep. , vol.184 , Issue.2-4 , pp. 229-257
    • Duplantier, B.1
  • 20
    • 24244442492 scopus 로고    scopus 로고
    • Conformally invariant fractals and potential theory
    • Duplantier, B.: Conformally invariant fractals and potential theory. Phys. Rev. Lett. 84(7), 1363-1367 (2000).
    • (2000) Phys. Rev. Lett. , vol.84 , Issue.7 , pp. 1363-1367
    • Duplantier, B.1
  • 22
    • 0000578291 scopus 로고
    • Structure and perimeters of percolation clusters
    • Grossman, T., Aharony, A.: Structure and perimeters of percolation clusters. J. Phys. A, Math. Gen. 19, L745-L751 (1986).
    • (1986) J. Phys. A, Math. Gen. , vol.19
    • Grossman, T.1    Aharony, A.2
  • 23
    • 67650908897 scopus 로고    scopus 로고
    • Discretely holomorphic parafermions and integrable loop models
    • arXiv: 0810. 5037v2 [math-ph]
    • Ikhlef, Y., Cardy, J.: Discretely holomorphic parafermions and integrable loop models. J. Phys. A 102001 (2009). arXiv: 0810. 5037v2 [math-ph].
    • (2009) J. Phys. A , pp. 102001
    • Ikhlef, Y.1    Cardy, J.2
  • 24
    • 3543011408 scopus 로고    scopus 로고
    • A guide to stochastic Loewner evolution and its applications
    • arXiv:math-ph/0312056v3
    • Kager, W., Nienhuis, B.: A guide to stochastic Loewner evolution and its applications. J. Stat. Phys. 115, 1149-1229 (2004). arXiv: math-ph/0312056v3.
    • (2004) J. Stat. Phys. , vol.115 , pp. 1149-1229
    • Kager, W.1    Nienhuis, B.2
  • 25
    • 0034345586 scopus 로고    scopus 로고
    • Conformal invariance of domino tiling
    • arXiv:math-ph/9910002v1
    • Kenyon, R.: Conformal invariance of domino tiling. Ann. Probab. 28, 759-795 (2000). arXiv: math-ph/9910002v1.
    • (2000) Ann. Probab. , vol.28 , pp. 759-795
    • Kenyon, R.1
  • 26
    • 0034341450 scopus 로고    scopus 로고
    • Universality and conformal invariance for the Ising model in domains with boundary
    • Langlands, R., Lewis, M.-A., Saint-Aubin, Y.: Universality and conformal invariance for the Ising model in domains with boundary. J. Stat. Phys. 98, 131-244 (2000).
    • (2000) J. Stat. Phys. , vol.98 , pp. 131-244
    • Langlands, R.1    Lewis, M.-A.2    Saint-Aubin, Y.3
  • 27
    • 79952703682 scopus 로고    scopus 로고
    • Worm Monte Carlo study of the honeycomb-lattice loop model
    • arXiv:1011.1980v2 [cond-mat.stat-mech]
    • Liu, Q., Deng, Y., Garoni, T. M.: Worm Monte Carlo study of the honeycomb-lattice loop model. Nucl. Phys. B 846, 283-315 (2011). arXiv: 1011. 1980v2 [cond-mat. stat-mech].
    • (2011) Nucl. Phys. B , vol.846 , pp. 283-315
    • Liu, Q.1    Deng, Y.2    Garoni, T.M.3
  • 28
    • 45149136697 scopus 로고
    • Negative fractal dimensions and multifractals
    • Mandelbrot, B. B.: Negative fractal dimensions and multifractals. Physica A 163, 306-315 (1990).
    • (1990) Physica A , vol.163 , pp. 306-315
    • Mandelbrot, B.B.1
  • 29
    • 0001371369 scopus 로고
    • Critical and multicritical O(n) models
    • Nienhuis, B.: Critical and multicritical O(n) models. Physica A 163, 152-157 (1990).
    • (1990) Physica A , vol.163 , pp. 152-157
    • Nienhuis, B.1
  • 31
    • 0010028333 scopus 로고
    • Critical percolation on the torus
    • Pinson, T. H.: Critical percolation on the torus. J. Stat. Phys. 75, 1167-1177 (1994).
    • (1994) J. Stat. Phys. , vol.75 , pp. 1167-1177
    • Pinson, T.H.1
  • 32
    • 23844467552 scopus 로고    scopus 로고
    • Basic properties of SLE
    • arXiv:math/0106036v4 [math.PR]
    • Rohde, S., Schramm, O.: Basic properties of SLE. Ann. Math. 161, 883-924 (2005). arXiv: math/0106036v4 [math. PR].
    • (2005) Ann. Math. , vol.161 , pp. 883-924
    • Rohde, S.1    Schramm, O.2
  • 33
    • 65449149781 scopus 로고    scopus 로고
    • Geometric exponents, SLE and logarithmic minimal models
    • arXiv: 0809. 4806v2
    • Saint-Aubin, Y., Pearce, P. A., Rasmussen, J.: Geometric exponents, SLE and logarithmic minimal models. J. Stat. Mech. P02028 (2009). arXiv: 0809. 4806v2.
    • (2009) J. Stat. Mech.
    • Saint-Aubin, Y.1    Pearce, P.A.2    Rasmussen, J.3
  • 34
    • 0001193785 scopus 로고
    • Exact determination of the percolation hull exponent in two dimensions
    • Saleur, H., Duplantier, B.: Exact determination of the percolation hull exponent in two dimensions. Phys. Rev. Lett. 58, 2325-2328 (1987).
    • (1987) Phys. Rev. Lett. , vol.58 , pp. 2325-2328
    • Saleur, H.1    Duplantier, B.2
  • 35
    • 70449679135 scopus 로고    scopus 로고
    • Exploration trees and conformal loop ensembles
    • arXiv:math/0609167v2 [math.PR]
    • Sheffield, S.: Exploration trees and conformal loop ensembles. Duke Math. J. 147(1), 79-129 (2006). arXiv: math/0609167v2 [math. PR].
    • (2006) Duke Math. J. , vol.147 , Issue.1 , pp. 79-129
    • Sheffield, S.1
  • 36
    • 0041869040 scopus 로고    scopus 로고
    • Critical percolation in the plane: conformal invariance. Cardy's formula, scaling limits
    • Smirnov, S.: Critical percolation in the plane: conformal invariance. Cardy's formula, scaling limits. C. R. Acad. Sci. Paris Sér. I Math. 333, 239-244 (2001).
    • (2001) C. R. Acad. Sci. Paris Sér. I Math. , vol.333 , pp. 239-244
    • Smirnov, S.1
  • 37
    • 77957693837 scopus 로고    scopus 로고
    • Conformal invariance in random cluster models. I. Holomorphic fermions in the Ising model
    • arXiv:0708.0039v1 [math-ph]
    • Smirnov, S.: Conformal invariance in random cluster models. I. Holomorphic fermions in the Ising model. Ann. Math. 172, 1435-1467 (2010). arXiv: 0708. 0039v1 [math-ph].
    • (2010) Ann. Math. , vol.172 , pp. 1435-1467
    • Smirnov, S.1
  • 38
    • 30544439717 scopus 로고
    • Cluster shapes at the percolation threshold: an effective cluster dimensionality and its connection with critical-point exponents
    • Stanley, H. E.: Cluster shapes at the percolation threshold: an effective cluster dimensionality and its connection with critical-point exponents. J. Phys. A, Math. Gen. 10, L211-L220 (1977).
    • (1977) J. Phys. A, Math. Gen. , vol.10
    • Stanley, H.E.1
  • 39
    • 33747349191 scopus 로고
    • Nonuniversal critical dynamics in Monte Carlo simulations
    • Swendsen, R. H., Wang, J.-S.: Nonuniversal critical dynamics in Monte Carlo simulations. Phys. Rev. Lett. 58(2), 86-88 (1987).
    • (1987) Phys. Rev. Lett. , vol.58 , Issue.2 , pp. 86-88
    • Swendsen, R.H.1    Wang, J.-S.2
  • 40
    • 0002032987 scopus 로고
    • Fractal dimensions of Potts clusters
    • Vanderzande, C.: Fractal dimensions of Potts clusters. J. Phys. A, Math. Gen. 25, L75-L80 (1992).
    • (1992) J. Phys. A, Math. Gen. , vol.25
    • Vanderzande, C.1
  • 41
    • 47749118683 scopus 로고    scopus 로고
    • The conformally invariant measure on self-avoiding loops
    • arXiv:math/0511605v3 [math.PR]
    • Werner, W.: The conformally invariant measure on self-avoiding loops. J. Am. Math. Soc. 21, 137-169 (2008). arXiv: math/0511605v3 [math. PR].
    • (2008) J. Am. Math. Soc. , vol.21 , pp. 137-169
    • Werner, W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.