9 research outputs found
Improved Phenomenological Renormalization Schemes
An analysis is made of various methods of phenomenological renormalization
based on finite-size scaling equations for inverse correlation lengths, the
singular part of the free energy density, and their derivatives. The analysis
is made using two-dimensional Ising and Potts lattices and the
three-dimensional Ising model. Variants of equations for the phenomenological
renormalization group are obtained which ensure more rapid convergence than the
conventionally used Nightingale phenomenological renormalization scheme. An
estimate is obtained for the critical finite-size scaling amplitude of the
internal energy in the three-dimensional Ising model. It is shown that the
two-dimensional Ising and Potts models contain no finite-size corrections to
the internal energy so that the positions of the critical points for these
models can be determined exactly from solutions for strips of finite width. It
is also found that for the two-dimensional Ising model the scaling finite-size
equation for the derivative of the inverse correlation length with respect to
temperature gives the exact value of the thermal critical exponent.Comment: 14 pages with 1 figure in late
Quantum Correlations in NMR systems
In conventional NMR experiments, the Zeeman energy gaps of the nuclear spin
ensembles are much lower than their thermal energies, and accordingly exhibit
tiny polarizations. Generally such low-purity quantum states are devoid of
quantum entanglement. However, there exist certain nonclassical correlations
which can be observed even in such systems. In this chapter, we discuss three
such quantum correlations, namely, quantum contextuality, Leggett-Garg temporal
correlations, and quantum discord. In each case, we provide a brief theoretical
background and then describe some results from NMR experiments.Comment: 21 pages, 7 figure