Title




Temperaturetime duality exemplified by Ising magnets and quantumchemical many electron theory
 
Author




 
Abstract




In this work, we first present a detailed analysis of temperaturetime 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 secondorder 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 4fold 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 Jordanvon NeumannWigner procedure. We then turn to discuss quite briefly temperaturetime duality in quantumchemical manyelectron theory. We find that one can use the known onedimensional 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. 
 
Language




English
 
Source (journal)




Journal of mathematical chemistry.  Basel
 
Publication




Basel
:
2011
 
ISSN




02599791
 
Volume/pages




49
:7
(2011)
, p. 12831290
 
ISI




000292816000007
 
Full text (Publisher's DOI)




 
