Effective Critical Exponents from Finite Temperature Renormalization Group

1996/04/30 by Michael Strickland, Strickland, Michael, Sen-Ben Liao +2
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th

paper · pdf · doi:10.48550/arxiv.hep-th/9604192

RevTeX, 8 pages, Short version of hep-th/9604125

arxiv created 1996/04/30 · openalex publication_date 1996/04/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Effective critical exponents for the λϕ⁴ scalar field theory are calculated as a function of the renormalization group block size k_o^-1 and inverse critical temperature β_c. Exact renormalization group equations are presented up to first order in the derivative expansion and numerical solutions are obtained with and without polynomial expansion of the blocked potential. For a finite temperature system in d dimensions, it is shown that β_c = β_c k_o determines whether the d-dimensional (β_c << 1) or (d+1)-dimensional (β_c >> 1) fixed point governs the phase transition. The validity of a polynomial expansion of the blocked potential near criticality is also addressed.

Citations

• Lectures on Phase Transitions and the Renormalization Group

Related

• Approach to the lower critical dimension of the φ⁴ theory in the derivative expansion of the Functional Renormalization Group
• Finite-Temperature Renormalization Group Predictions: The Critical Temperature Exponents, and Amplitude Ratios
• Field theory near the critical temperature
• Critical Exponents from Dimensional Variation
• Massive ϕ⁴ Model at Finite Temperature -- Resummayion Procedure la RG Improvement --