SCALING BEHAVIOR OF CONFINED O(n) SYSTEMS INVOLVING LONG-RANGE INTERACTION

To explore the finite-size scaling in confined systems involving an interaction with long-range tail one needs the development of suitable mathematical techniques. In the present review we consider the scaling behavior of the finite O(n) model with long-range interaction that is widely used in the theory of classical and quantum phase transitions. We consider finite geometries subject to periodic boundary conditions. The present mathematical method may be used to compute different thermodynamic quantities such as: the free energy, the susceptibility, specific heat etc. Here, we present results for the susceptibility in different regions of the phase diagram. Furthermore, we investigate the effect of classical and quantum fluctuations and check various scaling hypotheses.