Harmonic crossover exponents in O(n) models with the pseudo-ε expansion approach

Physical Review B - Condensed Matter and Materials Physics

Volumn 71, Issue 6, 2005, Pages

  Calabrese, Pasquale ^a   Parruccini, Pietro ^b  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b UNIVERSITY OF BOLOGNA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ACCURACY; ANISOTROPY; ARTICLE; CALCULATION; ENERGY; MAGNETISM; MATHEMATICAL ANALYSIS; MODEL; PHASE TRANSITION; PHYSICS; TEMPERATURE SENSITIVITY; TENSION; THEORY;

EID: 16344391782     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.71.064416     Document Type: Article

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80. For the standard exponents we have taken the following numerical results: v=0.5874(2) for N=0 [T. Prellberg, J. Phys. A 34, L599 (2001)] and γ=1.1575(6) [S. Caracciolq, M. S. Causo, and A. Pelissetto, Phys. Rev. E 57, R1215 (1998)], v=0.63012(16) for N=1 [M. Campostrini, A. Pelissetto, P. Rossi, and E. Vicari, ibid. 65, 066127 (2002)] v=0.67155(27) for N=2 [M. Campostrini, M. Hasenbusch, A. Pelissetto, P. Rossi, and E. Vicari, Phys. Rev. B 63, 214503 (2001)], v=0.7112(5) for N=3 [M. Campostrini, M. Hasenbusch, A. Pelissetto, P. Rossi, and E. Vicari, ibid. 65, 144520 (2002)], v=0.749(2) for N=4 [M. Hasenbusch, J. Phys. A 34, 8221 (2001)] v=0.764(2) for N=5 [A. Butti and F. Parisen Toldin, Nucl. Phys. B 704, 527 (2005)], and 0.911 for N=16 (Ref. 53). In three dimensions α is given by the scaling law 2-α=3v. Other numerical estimates can be found in Ref. 1.
81. For the standard exponents we have taken the following numerical results: v=0.5874(2) for N=0 [T. Prellberg, J. Phys. A 34, L599 (2001)] and γ=1.1575(6) [S. Caracciolq, M. S. Causo, and A. Pelissetto, Phys. Rev. E 57, R1215 (1998)], v=0.63012(16) for N=1 [M. Campostrini, A. Pelissetto, P. Rossi, and E. Vicari, ibid. 65, 066127 (2002)] v=0.67155(27) for N=2 [M. Campostrini, M. Hasenbusch, A. Pelissetto, P. Rossi, and E. Vicari, Phys. Rev. B 63, 214503 (2001)], v=0.7112(5) for N=3 [M. Campostrini, M. Hasenbusch, A. Pelissetto, P. Rossi, and E. Vicari, ibid. 65, 144520 (2002)], v=0.749(2) for N=4 [M. Hasenbusch, J. Phys. A 34, 8221 (2001)] v=0.764(2) for N=5 [A. Butti and F. Parisen Toldin, Nucl. Phys. B 704, 527 (2005)], and 0.911 for N=16 (Ref. 53). In three dimensions α is given by the scaling law 2-α=3v. Other numerical estimates can be found in Ref. 1.
82. For the standard exponents we have taken the following numerical results: v=0.5874(2) for N=0 [T. Prellberg, J. Phys. A 34, L599 (2001)] and γ=1.1575(6) [S. Caracciolq, M. S. Causo, and A. Pelissetto, Phys. Rev. E 57, R1215 (1998)], v=0.63012(16) for N=1 [M. Campostrini, A. Pelissetto, P. Rossi, and E. Vicari, ibid. 65, 066127 (2002)] v=0.67155(27) for N=2 [M. Campostrini, M. Hasenbusch, A. Pelissetto, P. Rossi, and E. Vicari, Phys. Rev. B 63, 214503 (2001)], v=0.7112(5) for N=3 [M. Campostrini, M. Hasenbusch, A. Pelissetto, P. Rossi, and E. Vicari, ibid. 65, 144520 (2002)], v=0.749(2) for N=4 [M. Hasenbusch, J. Phys. A 34, 8221 (2001)] v=0.764(2) for N=5 [A. Butti and F. Parisen Toldin, Nucl. Phys. B 704, 527 (2005)], and 0.911 for N=16 (Ref. 53). In three dimensions α is given by the scaling law 2-α=3v. Other numerical estimates can be found in Ref. 1.
83. For the standard exponents we have taken the following numerical results: v=0.5874(2) for N=0 [T. Prellberg, J. Phys. A 34, L599 (2001)] and γ=1.1575(6) [S. Caracciolq, M. S. Causo, and A. Pelissetto, Phys. Rev. E 57, R1215 (1998)], v=0.63012(16) for N=1 [M. Campostrini, A. Pelissetto, P. Rossi, and E. Vicari, ibid. 65, 066127 (2002)] v=0.67155(27) for N=2 [M. Campostrini, M. Hasenbusch, A. Pelissetto, P. Rossi, and E. Vicari, Phys. Rev. B 63, 214503 (2001)], v=0.7112(5) for N=3 [M. Campostrini, M. Hasenbusch, A. Pelissetto, P. Rossi, and E. Vicari, ibid. 65, 144520 (2002)], v=0.749(2) for N=4 [M. Hasenbusch, J. Phys. A 34, 8221 (2001)] v=0.764(2) for N=5 [A. Butti and F. Parisen Toldin, Nucl. Phys. B 704, 527 (2005)], and 0.911 for N=16 (Ref. 53). In three dimensions α is given by the scaling law 2-α=3v. Other numerical estimates can be found in Ref. 1.
84. For the standard exponents we have taken the following numerical results: v=0.5874(2) for N=0 [T. Prellberg, J. Phys. A 34, L599 (2001)] and γ=1.1575(6) [S. Caracciolq, M. S. Causo, and A. Pelissetto, Phys. Rev. E 57, R1215 (1998)], v=0.63012(16) for N=1 [M. Campostrini, A. Pelissetto, P. Rossi, and E. Vicari, ibid. 65, 066127 (2002)] v=0.67155(27) for N=2 [M. Campostrini, M. Hasenbusch, A. Pelissetto, P. Rossi, and E. Vicari, Phys. Rev. B 63, 214503 (2001)], v=0.7112(5) for N=3 [M. Campostrini, M. Hasenbusch, A. Pelissetto, P. Rossi, and E. Vicari, ibid. 65, 144520 (2002)], v=0.749(2) for N=4 [M. Hasenbusch, J. Phys. A 34, 8221 (2001)] v=0.764(2) for N=5 [A. Butti and F. Parisen Toldin, Nucl. Phys. B 704, 527 (2005)], and 0.911 for N=16 (Ref. 53). In three dimensions α is given by the scaling law 2-α=3v. Other numerical estimates can be found in Ref. 1.
85. For the standard exponents we have taken the following numerical results: v=0.5874(2) for N=0 [T. Prellberg, J. Phys. A 34, L599 (2001)] and γ=1.1575(6) [S. Caracciolq, M. S. Causo, and A. Pelissetto, Phys. Rev. E 57, R1215 (1998)], v=0.63012(16) for N=1 [M. Campostrini, A. Pelissetto, P. Rossi, and E. Vicari, ibid. 65, 066127 (2002)] v=0.67155(27) for N=2 [M. Campostrini, M. Hasenbusch, A. Pelissetto, P. Rossi, and E. Vicari, Phys. Rev. B 63, 214503 (2001)], v=0.7112(5) for N=3 [M. Campostrini, M. Hasenbusch, A. Pelissetto, P. Rossi, and E. Vicari, ibid. 65, 144520 (2002)], v=0.749(2) for N=4 [M. Hasenbusch, J. Phys. A 34, 8221 (2001)] v=0.764(2) for N=5 [A. Butti and F. Parisen Toldin, Nucl. Phys. B 704, 527 (2005)], and 0.911 for N=16 (Ref. 53). In three dimensions α is given by the scaling law 2-α=3v. Other numerical estimates can be found in Ref. 1.
86. For the standard exponents we have taken the following numerical results: v=0.5874(2) for N=0 [T. Prellberg, J. Phys. A 34, L599 (2001)] and γ=1.1575(6) [S. Caracciolq, M. S. Causo, and A. Pelissetto, Phys. Rev. E 57, R1215 (1998)], v=0.63012(16) for N=1 [M. Campostrini, A. Pelissetto, P. Rossi, and E. Vicari, ibid. 65, 066127 (2002)] v=0.67155(27) for N=2 [M. Campostrini, M. Hasenbusch, A. Pelissetto, P. Rossi, and E. Vicari, Phys. Rev. B 63, 214503 (2001)], v=0.7112(5) for N=3 [M. Campostrini, M. Hasenbusch, A. Pelissetto, P. Rossi, and E. Vicari, ibid. 65, 144520 (2002)], v=0.749(2) for N=4 [M. Hasenbusch, J. Phys. A 34, 8221 (2001)] v=0.764(2) for N=5 [A. Butti and F. Parisen Toldin, Nucl. Phys. B 704, 527 (2005)], and 0.911 for N=16 (Ref. 53). In three dimensions α is given by the scaling law 2-α=3v. Other numerical estimates can be found in Ref. 1.
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90. 2 as obtained by means of scaling relations (for the exponent v we take the value in Ref. 54) and the uncertainty is the maximum deviation. Obviously, the quoted error bars are only indicative.
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