Unique Trajectory Method in Migdal Renormalization Group Approach and Crossover Phenomena

Abstract

Migdal renormalization group approach, combined with Wilson· Kogut topological argu· ment, is applied to four dimensional lattice gauge theory of finite subgroup [(120) of 5U(2). i) A slight (compared with the Monte Carlo results) but clear crossover from strong coupling regime to weak coupling regime is observed for the Wilson action. ii) For mixed action, of the fundamental and the adjoint representation, a clearer stepwise transition, suggesting first order phase transition, is found at 1:S/:Iab:S3 (where /:lab denotes the bare inverse coupling constant of the adjoint representation). This stepwise transition changes into crossover for smaller /:lab iii) There are four critical lines in (/:1/, /:I:) plane starting from a quadruple point (/:1/ ~ 0.75, /:I: ~ 3.2) where /:1/ denotes the bare inverse coupling constant of the fundamental representation; 1) 50(3) critical line, 2) Z(2) critical line, 3) a critical line due to the discreteness of [(120), 4) a critical line related to crossover. In this investigation, the unique trajectory of renormal· ization group is very important and plays a powerful role in finding crossover and stepwise transition.