Phases, phase transitions and spin dynamics in strongly correlated electron systems, from antiferromagnets to HT_C superconductors: NMR-NQR insights

Abstract

Phase transitions (PT) are typical collective phenomena occurring in many-body systems with interparticle interactions. A rather general description of the PT’s and of the accompanying “critical dynamics” can be given in the framework of Landau-type statistical theory, which includes more specific theories such as the Weiss mean field theory for magnetic systems and the Van der Waals theory for fluids. This approach is suited for second order or slightly first-order PT³.

At the transition one observe “anomalous” behaviour (such as divergencies or tendencies to zero) of the response functions, namely the derivatives of the thermodynamical densities (e.g. magnetization, particle density, entropy) with respect to the conjugate fields (magnetic or electric fields, pressure, temperature). That behaviour reflects the onset of correlation and slowing down of the fluctuations around the equilibrium values, fluctuations in turn driven by some microscopic critical dynamics. The order of a transition is related to the order of the derivative of the thermodynamical potentials which display discontinuity at the critical point. First order, when the first derivatives with respect to the conjugate variable display discontinuity. Tipically this classification refers to the order parameter, namely the density going toward zero when the critical point is approached along the coexistence curve. For second order transition only the second derivatives of the thermodinamical potential have discontinuity at the critical point. At variance, the order parameter goes to zero with continuity on approaching the critical point.