scholarly journals Derivative expansion of the renormalization group in O(N) scalar field theory

1998 ◽  
Vol 509 (3) ◽  
pp. 637-661 ◽  
Author(s):  
Tim R Morris ◽  
Michael D Turner
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Scalar Field ◽  
Derivative Expansion ◽  
Scalar Field Theory

scholarly journals HALPERN-HUANG DIRECTIONS IN EFFECTIVE SCALAR FIELD THEORY

1996 ◽  
Vol 11 (37) ◽  
pp. 2915-2919 ◽  
Author(s):  
VIPUL PERIWAL
Keyword(s):  
Field Theory ◽  
Fixed Point ◽  
Renormalization Group ◽  
Scalar Field ◽  
Cutoff Function ◽  
Scalar Field Theory ◽  
Wilson Renormalization Group

Halpern and Huang recently showed that there are relevant directions in the space of interactions at the Gaussian fixed point. We show that their result can be derived from Polchinski’s form of the Wilson renormalization group. The derivation shows that the existence of these directions is independent of the cutoff function used.

scholarly journals CONVERGENCE OF DERIVATIVE EXPANSIONS IN SCALAR FIELD THEORY

2001 ◽  
Vol 16 (11) ◽  
pp. 2095-2100 ◽  
Author(s):  
TIM R. MORRIS ◽  
JOHN F. TIGHE
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Flow Equation ◽  
Renormalisation Group ◽  
Massless Scalar ◽  
Derivative Expansion ◽  
Scalar Field Theory ◽  
Β Function

The convergence of the derivative expansion of the exact renormalisation group is investigated via the computation of the β function of massless scalar λφ4 theory. The derivative expansion of the Polchinski flow equation converges at one loop for certain fast falling smooth cutoffs. Convergence of the derivative expansion of the Legendre flow equation is trivial at one loop, but also can occur at two loops and in particular converges for an exponential cutoff.

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