Nonuniversal critical behavior and its suppression by quantum fluctuations

Abstract

The phase transition at $T_c=0\mathrm{}$, caused by variation of parameters in a lattice dynamic system, is studied by means of classical and quantum-statistical mechanics. We calculate the critical exponents explicitly. They differ from those for $T_c\ne 0$. Within the frame of classical statistical mechanics they are nonuniversal, depending on a parameter. This feature is suppressed, however, by quantum fluctuations. The quantum-mechanical $T_c=0\mathrm{}$ critical point for a $d$-dimensional system corresponds to the Wilson fix point of a ($d+1\mathrm{}$)-dimensional system.