The coverage of the 2016 Nobel Prize in Physics (Physics Today, December 2016, page 14) was enjoyable, particularly because my colleague David Thouless shared in the prize. The piece states, correctly, that in the 1930s “Rudolf Peierls argued convincingly that in [two-dimensional] materials, the thermal motions of atoms would prevent long-range order from being established.” However, the case Peierls made in his 1935 article1 was a variant of a 1930 argument by Felix Bloch2 that thermally excited magnons would prevent the establishment of long-range order in two-dimensional Heisenberg magnets.

1.
R. E.
Peierls
,
Ann. Inst. Henri Poincare
5
,
177
(
1935
). http://www.numdam.org/item?id=AIHP_1935__5_3_177_0
3.
Sung
Chang
,
Physics Today
69
(
12
),
14
(
2016
).