Temperature Renormalization Group and Resummation
  The temperature renormalization group equation (TRGE) is compared with a diagrammatic expansion for the $(\phi^4)_4$-theory. It is found that the one-loop TRGE resums the leading powers of temperature for the effective mass. A two-loop contribution to TRGE is required to do the leading resummation for the coupling constant. It is also shown that the higher order TRGE resums subleading powers of temperature. 
Per Elmfors