Logarithmic corrections to the mean-field theory of tricritical points

Abstract

The logarithmic corrections to the mean-field theory of symmetrical tricritical points in three dimensions are derived using a graphical method. The free energy, equation of state, and other thermodynamic quantities are obtained in the disordered and ordered phases. The difference in thermodynamic potential between the ordered and disordered states takes the form $G={\ensuremath{\mu}}^{\frac{3}{2}}{L}^{\frac{1}{2}}(r)\ifmmode\times\else\texttimes\fi{}g(Q{\ensuremath{\mu}}^{\frac{\ensuremath{-}1}{2}}{L}^{\frac{1}{2}\ensuremath{-}p}(r),\ensuremath{\zeta}{\ensuremath{\mu}}^{\frac{\ensuremath{-}5}{4}}{L}^{\frac{\ensuremath{-}1}{4}}(r))$, where the fields $\ensuremath{\mu}$ and $Q$ are measured normal and tangential to the critical line, respectively, $\ensuremath{\zeta}$ is the field which couples to the order parameter, $r$ is the inverse susceptibility, and $L(r)\ensuremath{\sim}\mathrm{ln}r$. The exponent $p$ depends on the number of components of the order parameter. This form for the free energy differs from that found by Wegner and Riedel.