A057374 -id:A057374 - cp's OEIS frontend

A057398 Low-temperature magnetization expansion for Kagome net (Potts model, q=3).

1, 0, 0, 0, -3, 0, -18, -12, -87, -120, -432, -840, -2883, -5208, -21378, -39876, -144507, -309456, -978888, -2349828, -6995931, -17727576, -52099902, -133195908, -389599548, -1010029956, -2921670744, -7740553548

Offset: 0

N. J. A. Sloane, Aug 30 2000

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I. Jensen, Table of n, a(n) for n = 0..67 (from link below)
I. Jensen, More terms

Cf. A057374-A057405.

A057404 Low-temperature specific heat expansion for Kagome net (Potts model, q=4).

Original entry on oeis.org

144, 0, 864, 1764, 3168, 18468, 25200, 117612, 301104, 736164, 3083472, 7009200, 26587584, 75949200, 220443768, 728295840, 1994796720, 6533132760, 19485485712, 59845160592, 189326190240, 566841960000

Offset: 0

N. J. A. Sloane, Aug 30 2000

nonn

I. Jensen, Table of n, a(n) for n = 0..54 (from link below)
I. Jensen, More terms
Index entries for sequences related to specific heat

Cf. A057374-A057405.

A007270 Low-temperature series for magnetization in zero-field 3-state Potts model on cubic lattice.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, -3, 0, 0, 0, -18, -18, 42, 0, -135, -270, 477, 648, -1980, -2988, 4140, 14052, -21690, -52920, 55020, 201852, -162774, -914538, 555750, 3229524, -1188327, -13301370, 1402686, 52334268, 95751, -195398208, -58983558, 761838084, 359664885, -2910516786, -1946958399, 10681132140, 10207745148, -40522674258

Offset: 0

Simon Plouffe

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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Andrey Zabolotskiy, Table of n, a(n) for n = 0..56 (using data from Vohwinkel)
A. J. Guttmann and I. G. Enting, Series studies of the Potts model: III. The 3-state model on the simple cubic lattice, J. Phys. A: Math. Gen., 27 (1994), 5801-5812; arXiv:hep-lat/9312083, 1993. See Table 1; note that row 36 is missing, see Kim.
Seung-Yeon Kim, Partition function zeros of the Q-state Potts model on the simple-cubic lattice, Nuclear Physics B, 637 (2002), 409-426; arXiv:cond-mat/0205451, 2002. See the note to Ref. [58].
S. Miyashita, D. D. Betts and C. J. Elliott, High-field series expansions and critical properties for the three-state Potts model, J. Phys. A 12 (1979), 1605-1622.
C. Vohwinkel, Yet another way to obtain low temperature expansions for discrete spin systems, Physics Letters B, 301 (1993), 208-212; arXiv:hep-lat/9211052, 1992. See Table 4: multiply by 3/2 to get this sequence.

Cf. other structures: A007271 (b.c.c. lattice), A057374 (square lattice), A057382 (hexagonal lattice), A057390 (honeycomb net), A057398 (kagome net). Cf. A002929 (Ising model).

a(30) corrected, terms a(34) and beyond added from Guttmann & Enting by Andrey Zabolotskiy, Feb 06 2022

Missing term a(36) inserted, name clarified by Andrey Zabolotskiy, Nov 17 2024

A057376 Low-temperature specific heat expansion for square lattice (Potts model, q=3).

Original entry on oeis.org

32, 0, 144, 196, 256, 1944, 1600, 7260, 24864, 21632, 164640, 265500, 657408, 2659956, 3730320, 16136700, 36340960, 84457380, 289921808, 592348808, 1815681792, 4836460000, 11458859776, 35005107420, 84260881600

Offset: 0

N. J. A. Sloane, Aug 29 2000

nonn

I. Jensen, Table of n, a(n) for n = 0..67 (from link below)
I. Jensen, More terms
Index entries for sequences related to specific heat

Cf. A057374-A057405.

A057377 Low-temperature partition function expansion for square lattice (Potts model, q=3).

Original entry on oeis.org

1, 0, 0, 0, 2, 0, 4, 4, 6, 24, 24, 68, 190, 192, 904, 1420, 3106, 9940, 14572, 49268, 102886, 225004, 652940, 1301256, 3513806, 8591792, 19326248, 52781148, 120709472, 306339824, 779682608, 1852672272, 4847112666, 11876028924

Offset: 0

N. J. A. Sloane, Aug 29 2000

nonn

I. Jensen, Table of n, a(n) for n = 0..71 (from link below)
I. Jensen, More terms

Cf. A057374-A057405.

A057379 Low-temperature susceptibility expansion for square lattice (Potts model, q=4).

Original entry on oeis.org

3, 0, 24, 48, 120, 648, 1608, 4176, 21093, 38064, 175608, 494616, 1365726, 5077200, 13549704, 43359768, 140590629, 389348688, 1296882504, 3834279072, 11499126642, 36680416368, 107193301920, 333178056720

Offset: 0

N. J. A. Sloane, Aug 30 2000

nonn

I. Jensen, Table of n, a(n) for n = 0..55 (from link below)
Ian G. Enting and Anthony J. Guttmann, Susceptibility amplitudes for the three- and four-state Potts models, Physica A, 321 (2003), 90-107.
I. Jensen, More terms

Cf. A057374-A057405.

A057380 Low-temperature specific heat expansion for square lattice (Potts model, q=4).

Original entry on oeis.org

48, 0, 216, 588, -96, 5832, 4800, 13068, 115776, 32448, 664440, 1736100, 1757760, 18387336, 24467184, 90326532, 379958640, 535402224, 2924464488, 7189478184, 17099776512, 73614120000, 153395478288, 528792612984

Offset: 0

N. J. A. Sloane, Aug 30 2000

sign

I. Jensen, Table of n, a(n) for n = 0..55 (from link below)
I. Jensen, More terms
Index entries for sequences related to specific heat

Cf. A057374-A057405.

A057381 Low-temperature partition function expansion for square lattice (Potts model, q=4).

Original entry on oeis.org

1, 0, 0, 0, 3, 0, 6, 12, 3, 72, 66, 144, 822, 480, 3624, 8508, 10482, 65856, 94794, 289452, 1008420, 1561032, 6503532, 15224016, 34976979, 125988144, 263308986, 805096764, 2319752694, 5402283396, 17415097542, 44310604860

Offset: 0

N. J. A. Sloane, Aug 30 2000

nonn

I. Jensen, Table of n, a(n) for n = 0..59 (from link below)
I. Jensen, More terms

Cf. A057374-A057405.

A057384 Low-temperature specific heat expansion for hexagonal lattice (Potts model, q=3).

Original entry on oeis.org

72, 0, 0, 0, 600, 726, -1440, 0, 7056, 8100, -13824, -20808, 94176, 119130, -196800, -291942, 917664, 1986924, -2389248, -5092500, 10788960, 26041338, -21643104, -81270876, 111771360, 369058596, -215519232, -1109316384

Offset: 0

N. J. A. Sloane, Aug 30 2000

sign

The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice.

I. Jensen, Table of n, a(n) for n = 0..63 (from link below)
I. Jensen, More terms
G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2
Index entries for sequences related to specific heat

Cf. A057374-A057405.

A057385 Low-temperature partition function expansion for hexagonal lattice (Potts model, q=3).

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 6, 6, -8, 0, 36, 36, -42, -60, 272, 330, -402, -554, 1758, 3564, -3320, -7056, 14616, 33426, -21498, -83640, 111856, 354612, -158802, -884208, 758088, 3744582, -734260, -9805608, 4839270, 38734736, 2364180

Offset: 0

N. J. A. Sloane, Aug 30 2000

sign

The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice.

I. Jensen, Table of n, a(n) for n = 0..69 (from link below)
I. Jensen, More terms
G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2

Cf. A057374-A057405.

cp's OEIS Frontend

A057398 Low-temperature magnetization expansion for Kagome net (Potts model, q=3).

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A057404 Low-temperature specific heat expansion for Kagome net (Potts model, q=4).

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A007270 Low-temperature series for magnetization in zero-field 3-state Potts model on cubic lattice.

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A057376 Low-temperature specific heat expansion for square lattice (Potts model, q=3).

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A057377 Low-temperature partition function expansion for square lattice (Potts model, q=3).

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A057379 Low-temperature susceptibility expansion for square lattice (Potts model, q=4).

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A057380 Low-temperature specific heat expansion for square lattice (Potts model, q=4).

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A057381 Low-temperature partition function expansion for square lattice (Potts model, q=4).

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A057384 Low-temperature specific heat expansion for hexagonal lattice (Potts model, q=3).

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A057385 Low-temperature partition function expansion for hexagonal lattice (Potts model, q=3).

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