cp's OEIS Frontend

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

%I A007270 M2194 #24 Nov 19 2024 01:04:23
%S A007270 1,0,0,0,0,0,-3,0,0,0,-18,-18,42,0,-135,-270,477,648,-1980,-2988,4140,
%T A007270 14052,-21690,-52920,55020,201852,-162774,-914538,555750,3229524,
%U A007270 -1188327,-13301370,1402686,52334268,95751,-195398208,-58983558,761838084,359664885,-2910516786,-1946958399,10681132140,10207745148,-40522674258
%N A007270 Low-temperature series for magnetization in zero-field 3-state Potts model on cubic lattice.
%D A007270 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A007270 Andrey Zabolotskiy, <a href="/A007270/b007270.txt">Table of n, a(n) for n = 0..56</a> (using data from Vohwinkel)
%H A007270 A. J. Guttmann and I. G. Enting, <a href="https://doi.org/10.1088/0305-4470/27/17/014">Series studies of the Potts model: III. The 3-state model on the simple cubic lattice</a>, J. Phys. A: Math. Gen., 27 (1994), 5801-5812; arXiv:<a href="https://arxiv.org/abs/hep-lat/9312083">hep-lat/9312083</a>, 1993. See Table 1; note that row 36 is missing, see Kim.
%H A007270 Seung-Yeon Kim, <a href="https://doi.org/10.1016/S0550-3213(02)00465-0">Partition function zeros of the Q-state Potts model on the simple-cubic lattice</a>, Nuclear Physics B, 637 (2002), 409-426; arXiv:<a href="https://arxiv.org/abs/cond-mat/0205451">cond-mat/0205451</a>, 2002. See the note to Ref. [58].
%H A007270 S. Miyashita, D. D. Betts and C. J. Elliott, <a href="https://doi.org/10.1088/0305-4470/12/9/026">High-field series expansions and critical properties for the three-state Potts model</a>, J. Phys. A 12 (1979), 1605-1622.
%H A007270 C. Vohwinkel, <a href="https://doi.org/10.1016/0370-2693(93)90690-J">Yet another way to obtain low temperature expansions for discrete spin systems</a>, Physics Letters B, 301 (1993), 208-212; arXiv:<a href="https://arxiv.org/abs/hep-lat/9211052">hep-lat/9211052</a>, 1992. See Table 4: multiply by 3/2 to get this sequence.
%Y A007270 Cf. other structures: A007271 (b.c.c. lattice), A057374 (square lattice), A057382 (hexagonal lattice), A057390 (honeycomb net), A057398 (kagome net). Cf. A002929 (Ising model).
%K A007270 sign
%O A007270 0,7
%A A007270 _Simon Plouffe_
%E A007270 a(30) corrected, terms a(34) and beyond added from Guttmann & Enting by _Andrey Zabolotskiy_, Feb 06 2022
%E A007270 Missing term a(36) inserted, name clarified by _Andrey Zabolotskiy_, Nov 17 2024