Dimensional Crossover and Effective Exponents

Abstract

We investigate the critical behavior of the lambda phi^4 theory defined on S^1 x R^d having two finite length scales beta, the circumference of S^1, and k^{-1}, the blocking scale introduced by the renormalization group transformation. By numerically solving the coupled differential RG equations for the finite-temperature blocked potential U_{beta,k}(Phi) and the wavefunction renormalization constant Z_{beta,k}(Phi), we demonstrate how the finite-size scaling variable betabar = beta k determines whether the phase transition is (d+1)- or d-dimensional in the limits betabar >> 1 and betabar << 1, respectively. For the intermediate values of betabar, finite-size effects play an important role. We also discuss the failure of the polynomial expansion of the effective potential near criticality.

24 pages, TeX, 8 figures in separate file, Updated version to appear in Nucl. Phys. B

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Cited by in corpus (18)

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• Lectures on the functional renormalization group method
• Renormalization Group Flow Equations and the Phase Transition in O(N)-models
• Optimization of Renormalization Group Flow
• Operator Cutoff Regularization and Renormalization Group in Yang-Mills Theory
• Application of Renormalization Group Techniques to a Homogeneous Bose Gas at Finite Temperature
• Critical Behavior and Dimension Crossover of Pion Superfluidity
• Investigation into O(N) Invariant Scalar Model Using Auxiliary-Mass Method at Finite Temperature
• Dynamics near the critical point: the hot renormalization group in quantum field theory
• Vacuum Structure of Twisted Scalar Field Theories on M^{D-1} \otimes S^1
• Critical Exponents and Critical Amplitude Ratio of The Scalar Model from Finite-temperature Field Theory
• Scheme Independence of Blocking Transformation in Finite-Temperature Renormalization Group
• Thermal Renormalization Group-Equations and the Phase-Transition of Scalar O(N)-Theories
• The Thermal Renormalization Group for Fermions, Universality, and the Chiral Phase-Transition
• Flow Equations for U_k and Z_k
• Scalar Field Theory with a Non-Standard Potential
• Self-consistent renormalization group flow
• The scaling region of the lattice O(N) sigma model at finite temperature