Finite temperature crossovers of the quantum Ising chain
The Ising chain in a transverse field is one of the simplest models which exhibits a quantum critical point.
The finite temperature crossovers in the vicinity of the critical point can be described rather
precisely, both for static (paper 1) and dynamic (paper 3) properties, as outlined in the figure below.
Finite temperature crossovers of the Ising chain in a transverse field.
The coupling g is a measure of the transverse field strength. For large g, all spins point along the
direction of the transverse field (+x) in the ground state; the excited states consist of "particles"
of flipped (x) spins moving in this background. For small g, the spins are ferromagnetically aligned
by their exchange interactions, and the "particles" are now domain walls separating regions of
oppositely aligned spins. In the quantum critical region, neither description is valid, and nontrivial scaling
arguments must be used.
PAPERS

Universal, finite temperature, crossover functions of
the quantum transition in the Ising chain in a transverse field, S.
Sachdev, Nuclear Physics B 464, 576 (1996); condmat/9509147.

Finite temperature correlations in the onedimensional
quantum Ising model, A. Leclair, F. Lesage, S. Sachdev, and H. Saleur,
Nuclear Physics B 482, 579 (1996); condmat/9606104.

Low temperature relaxational dynamics of the Ising chain
in a transverse field, S. Sachdev and A.P. Young, Physical Review Letters
78,
2220 (1997); condmat/9609185.

Finite temperature correlations of the Ising chain in
transverse field, S. Sachdev, Symposium on Exactly Soluble Models
in Statistical Mechanics: Historical Perspectives and Current Status,
C. King and F.Y. Wu eds., International Journal of Modern Physics B 11,
57 (1997).

Dynamics and transport near quantumcritical points,
S. Sachdev, Dynamical properties of unconventional magnetic systems,
A. Skjeltorp and D. Sherrington eds., NATO ASI Series E: Applied Sciences,
vol 349, Kluwer Academic, Dordrecht (1997); condmat/9705206.

Finite temperature dynamics near quantum phase transitions, S. Sachdev, keynote talk at the 11th International Conference on Recent
Progress in ManyBody Theories, UMIST, Manchester UK, 913 July,
2001, edited by Raymond F. Bishop, Tobias Brandes, Klaus A. Gernoth, Niels R. Walet and Yang Xian, World Scientific, Singapore (2002); condmat/0110161.

Quantum Fluctuations of the Transverse Field Ising Chain,
A. W. Kinross, M. Fu, T. J. Munsie, H. A. Dabkowska, G. M. Luke, S. Sachdev, and T. Imai, Physical Review X 4, 031008 (2014);
arXiv:1401.6917.
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