Monte Carlo and Renormalization Group Effective Potentials in Scalar Field Theories

Abstract

We study constraint effective potentials for various strongly interacting ${\varphi }^4$ theories. Renormalization group (RG) equations for these quantities are discussed and a heuristic development of a commonly used RG approximation is presented which stresses the relationships among the loop expansion, the Schwinger-Dyson method and the renormalization group approach. We extend the standard RG treatment to account explicitly for finite lattice effects. Constraint effective potentials are then evaluated using Monte Carlo (MC) techniques and careful comparisons are made with RG calculations. Explicit treatment of finite lattice effects is found to be essential in achieving quantitative agreement with the MC effective potentials. Excellent agreement is demonstrated for $d=3$ and $d=4$, O(1) and O(2) cases in both symmetric and broken phases.

16 pages, 4 figures appended to end of this file

References in corpus (7)

• The Exact Renormalisation Group and Approximate Solutions
• Critical Exponents from the Effective Average Action
• Derivative Expansion of the Exact Renormalization Group
• On Truncations of the Exact Renormalization Group
• Critical Exponents without the Epsilon Expansion
• Gradient Flows from an Approximation to the Exact Renormalization Group
• The Non-Trivial Effective Potential of the `Trivial' lambda Phi^4 Theory: A Lattice Test

Cited by in corpus (3)

• Spontaneous Symmetry Breaking and Proper-Time Flow Equations
• Renormalization Group Flow Equations for the Sigma Model
• Universality in the exact renormalization group: comparison to perturbation theory