A007270 Low-temperature series for magnetization in zero-field 3-state Potts model on cubic lattice. (Formerly M2194)

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

0,7

References

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

Links

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.

Crossrefs

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

Sequence in context: A377127 A228861 A057382 * A222896 A057387 A109898

Adjacent sequences: A007267 A007268 A007269 * A007271 A007272 A007273

Keyword

sign

Author

Simon Plouffe

Extensions

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

Status

approved