Temperature-time duality exemplified by Ising magnets and quantum-chemical many electron theory |
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Authors: | Z D Zhang N H March |
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Institution: | 1.Shenyang National Laboratory for Materials Science, Institute of Metal Research and International Centre for Materials Physics,Chinese Academy of Sciences,Shenyang,People’s Republic China;2.Department of Physics,University of Antwerp,Antwerp,Belgium;3.Oxford University,Oxford,England |
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Abstract: | In this work, we first present a detailed analysis of temperature-time duality in the 3D Ising model, by inspecting the resemblance
between the density operator in quantum statistical mechanics and the evolution operator in quantum field theory, with the
mapping β = (k
B
T)−1 → it. We point out that in systems like the 3D Ising model, for the nontrivial topological contributions, the time necessary
for the time averaging must be infinite, being comparable with or even much larger than the time of measurement of the physical
quantity of interest. The time averaging is equivalent to the temperature averaging. The phase transitions in the parametric
plane (β, it) are discussed, and a singularity (a second-order phase transition) is found to occur at the critical time t
c
, corresponding to the critical point β
c
(i.e, T
c
). It is necessary to use the 4-fold integral form for the partition function for the 3D Ising model. The time is needed to
construct the (3 + 1)D framework for the quaternionic sequence of Jordan algebras, in order to employ the Jordan-von Neumann-Wigner
procedure. We then turn to discuss quite briefly temperature-time duality in quantum-chemical many-electron theory. We find
that one can use the known one-dimensional differential equation for the Slater sum S(x, β) to write a corresponding form for the diagonal element of the Feynman propagator, again with the mapping β → it. |
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Keywords: | |
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