Three-dimensional (3D) Ising universality and temperature-time duality

Experimental data for critical exponents in some magnetic materials are compared with recent theoretical results on the three – dimensional (3D) Ising model based on two conjectures [Z.D. Zhang, Phil. Mag. 87 (2007) 5309.]. It is found that critical exponents in some bulk magnetic materials indeed form a 3D Ising universality. Our attention is then focused on the critical indices at fluid-fluid phase transition. We suggest to use the Zhang’s exponent β= 3/8 to fit the experimental data over the wider asymptotic region near the critical point of a fluid-fluid phase transition. The 3D Ising universality should exist for critical indices in a certain class of magnets and at fluid-fluid phase transition. We also 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= (kBT)-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, and 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 tc, corresponding to the critical point βc (i.e, Tc). 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.