The Quantum–Classical Crossover as Phase Transition

L. De Cesare, Ileana Rabuffo, Dimo I. Uzunov

The phase transition properties of the quantum spin{1/2 Ising model in a transverse magnetic eld are reconsidered with the help of the mean eld approximation, the Ginzburg criterion, and the renormalization group theory.A special attention is paid to the phase transitions whose properties are determined by variations of the external transverse eld and to the low{temperature phase transitions due to temperature variations.The classical{to{quantum crossover is investigated in details.A new crossover eect is established and discussed.

Artur Mendes Kur

L. De Cesare, L. Craco, Ileana Rabuffo +1 more

A method of investigation of dimensional crossover phenomena in the theory of phase transitions is illustrated for the nite{size crossover.The dimensional crossover phenomena in systems with quenched extended impurities and inhomogeneities as well as the classical{to{quantum crossover at extremely low temperatures are also discussed.The fundamental interrelationship between the effective dimensionality and the ratio of the relevant characteristic lengths of the system is established and applied to the description of dimensional crossover phenomena.

Yuval Ne’eman